Package 'shotGroups'

Description

The shotGroups package provides functions to read in, plot, statistically describe, analyze, and compare shooting data with respect to group shape, precision, and accuracy. This includes graphical methods, descriptive statistics, and inference tests using standard, but also non-parametric and robust statistical methods. Works with files exported by 'OnTarget PC/TDS', 'Silver Mountain' e-target, 'ShotMarker' e-target, or 'Taran', as well as with custom data files in text format. Supports inference from range statistics such as extreme spread. Includes web-based graphical user interface.

Details

Use help(package='shotGroups') for a list of all functions and links to the detailed help pages with information on options, usage and output. For further explanantions and an example walkthrough, see vignette('shotGroups').

Author(s)

Daniel Wollschlaeger

Maintainer: Daniel Wollschlaeger [email protected]

Examples

groupSpread(DFcciHV, dstTarget=100, conversion='yd2in', bootCI='none')

Description

Performs a comprehensive numerical and graphical analysis of a single group of bullet holes.

Usage

analyzeGroup(DF, xyTopLeft = TRUE, center = FALSE,
             dstTarget, conversion, bandW = 0.5,
             CEPtype = 'CorrNormal', bootCI = 'none')

Arguments

Details

By default, OnTarget PC/TDS' 'Export Point Data' places the origin of the absolute coordinate system in the top-left corner. In OnTarget TDS, this setting can be changed by checking the box 'Tools -> Options -> Options tab -> Data Export -> Invert Y-Axis on Export'. In that case, use xyTopLeft=FALSE. If groups appear to be upside-down, xyTopLeft is the setting to change.

Robust estimates for the group center and the covariance matrix of (x,y)-coordinates are from covMcd using the MCD algorithm.
This function is a wrapper for groupShape, groupLocation, and groupSpread.
If the data is missing information about the point of aim, (0,0) is assumed. If distance to target is missing, 100 is assumed.
The number of replicates for the reported bootstrap confidence intervals is at least 1499. If the BCa interval is reported, it is at least the number of points.

In addition to the numerical results listed below, this function produces the following diagrams:

• a combined plot for multivariate outlier identification as produced by aq.plot

• a scatterplot of the (x,y)-coordinates together with group center, circle with average distance to center, 50%-confidence ellipse - the latter also based on a robust estimate for the covariance matrix

• a scatterplot of the (x,y)-coordinates together with the minimum bounding box, minimum enclosing circle, and maximum group spread

• a chi-square Q-Q-plot for eyeballing multivariate normality as produced by chisq.plot, including a reference line with intercept 0 and slope 1

• a heatmap of a 2D-kernel density estimate for the (x,y)-coordinates as produced by smoothScatter together with group center and error ellipse based on a robust estimate for the covariance matrix

• a Q-Q-plot of x-coordinates for eyeballing normality

• a Q-Q-plot of y-coordinates for eyeballing normality

• a histogram of x-coordinates including a fitted normal distribution as well as a non-parametric kernel density estimate

• a histogram of y-coordinates including a fitted normal distribution as well as a non-parametric kernel density estimate

• a histogram of distances to group center including a fitted Rayleigh distribution as well as a non-parametric kernel density estimate

Value

A list with the results from the numerical analyses and statistical tests.

See Also

groupShape, groupLocation, groupSpread, compareGroups, getDistToCtr, getMaxPairDist, getBoundingBox, getMinBBox, getMinCircle, getConfEll, getCEP, getRayParam, getMOA, smoothScatter, chisq.plot, aq.plot, pcout, qqnorm, hist, kernel, shapiro.test, mvnorm.etest, anova.mlm, boot, boot.ci, covMcd

Examples

data(DFinch)

# select combined data from only first 2 series
DF  <- subset(DFinch, series %in% 1:2)
res <- analyzeGroup(DF, conversion='yd2in', bootCI='none')
names(res)
res$multNorm
res$corXY
res$ctrRob
res$ctrXci
res$ctrYci

Description

Combines a list of data frames (the result from using readDataOT1, readDataOT2, or readDataMisc with combine=FALSE) into one big data frame.

Usage

combineData(DFs)

Arguments

Details

Assumes that the data frames in the list have a non-empty set of shared variables. Among them at least either point.x, point.y or x, y defining the bullet holes. To be useful for functions analyzeGroup or compareGroups, the data frames should also have variables group, distance, aim.x, aim.y defining point of aim. If group is missing, it is set to 1.

Value

A data frame with the shared set of variables. In addition, it also contains factors identifying the original file (file), and a factor identifying all groups from different data frames (series).

See Also

readDataMisc, readDataOT1, readDataOT2, analyzeGroup, compareGroups

Examples

## combine list of data frames to one single data frame
data(DFlistCm)
DFcm <- combineData(DFlistCm)
str(DFcm)
head(DFcm)

Description

Numerically and graphically compare accuracy, precision, and distribution shape of up to 15 groups of bullet holes.

Usage

compareGroups(DF, plots = TRUE, xyTopLeft = TRUE, center = FALSE,
              ABalt = c('two.sided', 'less', 'greater'),
              Walt = c('two.sided', 'less', 'greater'),
              CEPtype = 'CorrNormal', CEPlevel = 0.5, CIlevel = 0.95,
              dstTarget, conversion)

Arguments

Details

By default, OnTarget PC/TDS' 'Export Point Data' places the origin of the absolute coordinate system in the top-left corner. In OnTarget TDS, this setting can be changed by checking the box 'Tools -> Options -> Options tab -> Data Export -> Invert Y-Axis on Export'. In that case, use xyTopLeft=FALSE. If groups appear to be upside-down, xyTopLeft is the setting to change.

OnTarget PC/TDS' Group variable identifies groups just within one file, whereas factor series is taken to number groups also across different original files. If your data was read with readDataOT1, readDataOT2 or readDataMisc, series is added automatically. For data from just one file, you can otherwise copy variable group to series in a data frame called shots with shots$series <- shots$group.
If the data is missing information about the point of aim, (0,0) is assumed. If distance to target is missing, 100 is assumed.

In addition to the numerical results listed below, this function produces the following diagrams:

• a scatterplot showing all groups as well as their respective center and confidence ellipse

• a scatterplot showing all groups as well as their respective (minimum) bounding box and maximum group spread

• a scatterplot showing all groups as well as their respective minimum enclosing circle and circle with average distance to center

• a boxplot for the distances to group center per group

• a stripchart showing the distances to group center per group together with the estimated Rayleigh mean radius and its confidence interval

If package shiny is installed, an interactive web app for this functionality can be run with runGUI("analyze").

Value

A list with the results from numerical comparisons and statistical tests.

See Also

analyzeGroup, getDistToCtr, getMaxPairDist, getMinBBox, getMinCircle, getCEP, getMOA, getRayParam, drawEllipse, anova.mlm, ansari_test, fligner_test, wilcox_test, kruskal_test

Examples

cmp <- compareGroups(DF300BLKhl, dstTarget=100, conversion='yd2in')
names(cmp)
cmp$ctr
cmp$meanDistToCtr
cmp$CEP
cmp$Kruskal

Description

Example of a data frame from one file with one group of bullet holes.

Usage

data(DF300BLK)

Format

A data frame with 20 observations on the following 9 variables.

group

a factor with level 1.

distance

a numerical vector giving the distance to the target.

aim.x

a numerical vector of x-coordinates giving the point of aim.

aim.y

a numerical vector of y-coordinates giving the of point of aim.

point.x

a numerical vector of absolute x-coordinates of bullet holes.

point.y

a numerical vector of absolute y-coordinates of bullet holes.

origin

a factor with level 1. This factor codes from which original output file the data is.

orgser

a factor with level 1.1. This factor results from droplevels(interaction(origin, group)), and codes each separate group across original files. The order of the factor levels is alphabetical.

series

a factor with level 1. This factor codes each separate group as defined by orgser, but more conveniently as a number that runs consecutively across original files.

distance.unit

Measurement unit distance to target

point.unit

Measurement unit (x,y)-coordinates

Details

One group of shooting a Noveske AR-15 rifle in 300BLK at 100yd with factory ammunition. The measurement unit for coordinates is inch, for distance yards.
This data frame is like those returned by readDataOT1, readDataOT2, or readDataMisc with option combine=TRUE.
Data courtesy of David Bookstaber, 2013. http://ballistipedia.com/

See Also

combineData, analyzeGroup, compareGroups

Examples

data(DF300BLK)
str(DF300BLK)

Description

Example of a data frame from one file with one group of bullet holes.

Usage

data(DF300BLK)

Format

A data frame with 60 observations on the following 9 variables.

group

a factor with level 1.

distance

a numerical vector giving the distance to the target.

aim.x

a numerical vector of x-coordinates giving the point of aim.

aim.y

a numerical vector of y-coordinates giving the of point of aim.

point.x

a numerical vector of absolute x-coordinates of bullet holes.

point.y

a numerical vector of absolute y-coordinates of bullet holes.

origin

a factor with level 1. This factor codes from which original output file the data is.

orgser

a factor with levels 1.1, 1.2, 1.3. This factor results from droplevels(interaction(origin, group)), and codes each separate group across original files. The order of the factor levels is alphabetical.

series

a factor with levels 1, 2, 3. This factor codes each separate group as defined by orgser, but more conveniently as a number that runs consecutively across original files.

distance.unit

Measurement unit distance to target

point.unit

Measurement unit (x,y)-coordinates

Details

Three groups of shooting a Noveske AR-15 rifle in 300BLK at 100yd with handloaded ammunition. The measurement unit for coordinates is inch, for distance yards.
This data frame is like those returned by readDataOT1, readDataOT2, or readDataMisc with option combine=TRUE.
Data courtesy of David Bookstaber, 2014. http://ballistipedia.com/

See Also

combineData, analyzeGroup, compareGroups

Examples

data(DF300BLK)
str(DF300BLK)

Description

Example of a data frame from one file with two groups of bullet holes.

Usage

data(DFcciHV)

Format

A data frame with 40 observations on the following 9 variables.

group

a factor with levels 1 2.

distance

a numerical vector giving the distance to the target.

aim.x

a numerical vector of x-coordinates giving the point of aim.

aim.y

a numerical vector of y-coordinates giving the of point of aim.

point.x

a numerical vector of absolute x-coordinates of bullet holes.

point.y

a numerical vector of absolute y-coordinates of bullet holes.

origin

a factor with levels 1. This factor codes from which original output file the data is.

orgser

a factor with levels 1.1 1.2. This factor results from droplevels(interaction(origin, group)), and codes each separate group across original files. The order of the factor levels is alphabetical.

series

a factor with levels 1 2. This factor codes each separate group as defined by orgser, but more conveniently as a number that runs consecutively across original files.

distance.unit

Measurement unit distance to target

point.unit

Measurement unit (x,y)-coordinates

Details

Two groups of shooting a PWS T3 rifle in .22LR at 100yd. The measurement unit for coordinates is inch, for distance yards.
This data frame is like those returned by readDataOT1, readDataOT2, or readDataMisc with option combine=TRUE.
Data courtesy of David Bookstaber, 2013. http://ballistipedia.com/

See Also

combineData, analyzeGroup, compareGroups

Examples

data(DFcciHV)
str(DFcciHV)

Description

Example of a combined data frame from several files exported by OnTarget PC/TDS, each with several groups of bullet holes.

Usage

data(DFcm)

Format

A data frame with 487 observations on the following 13 variables.

project.title

a character vector giving the OnTarget PC/TDS project title.

group

a factor with levels 1 2 3. This is the original Group variable as defined by OnTarget PC/TDS.

ammunition

a character vector describing the ammo.

distance

a numerical vector giving the distance to the target.

aim.x

a numerical vector of x-coordinates giving the point of aim.

aim.y

a numerical vector of y-coordinates giving the of point of aim.

center.x

a numerical vector of x-coordinates giving the group centers.

center.y

a numerical vector of y-coordinates giving the group centers.

point.x

a numerical vector of absolute x-coordinates of bullet holes.

point.y

a numerical vector of absolute y-coordinates of bullet holes.

origin

a factor with levels 1 2 3. This factor codes from which original output file the data is.

orgser

a factor with levels 1.1 2.1 3.1 1.2 2.2 3.2 1.3 2.3 3.3. This factor results from droplevels(interaction(origin, group)), and codes each separate group across original files. The order of the factor levels is alphabetical.

series

a factor with levels 1 2 3 4 5 6 7 8 9. This factor codes each separate group as defined by orgser, but more conveniently as a number that runs consecutively across original files.

distance.unit

Measurement unit distance to target

point.unit

Measurement unit (x,y)-coordinates

target

Character string "BDS9" indicating the target face. See targets.

Details

Several groups of shooting a 9x19mm pistol at 25m. The measurement unit for coordinates is cm, for distance meters.
This data frame is like those returned by readDataOT1, readDataOT2, or readDataMisc with option combine=TRUE.

See Also

combineData, analyzeGroup, compareGroups

Examples

data(DFcm)
str(DFcm)

Description

Lookup table for the distribution of range statistics and Rayleigh sigma from a Monte Carlo simulation of circular bivariate normal shot groups with 0 mean and variance 1 in both directions. Includes the first four moments and several quantiles of the distribution of extreme spread, figure of merit, bounding box diagonal, and Rayleigh sigma for each combination of number of shots per group and number of groups, repeated 10 million times.

Usage

data(DFdistr)

Format

A data frame with 590 observations on the following 77 variables.

n

number of shots in each group. One of 2, 3, ..., 49, 50, 45, ..., 95, 100.

nGroups

number of groups with individual simulated range statistics that were averaged over to yield the final value. One of 1, 2, ..., 9, 10.

nShots

total number of shots, i.e., n*nGroups.

ES_M

Extreme spread mean over all Monte Carlo simulations

ES_V

Extreme spread variance over all Monte Carlo simulations

ES_SD

Extreme spread standard deviation over all Monte Carlo simulations

ES_CV

Extreme spread coefficient of variation over all Monte Carlo simulations

ESSQ_M

Squard extreme spread mean over all Monte Carlo simulations

ESSQ_V

Squared extreme spread variance over all Monte Carlo simulations

ES_SKEW

Extreme spread skewness over all Monte Carlo simulations (smoothed)

ES_KURT

Extreme spread kurtosis over all Monte Carlo simulations (smoothed)

ES_MED

Extreme spread median (50% quantile) over all Monte Carlo simulations

ES_Q005

Extreme spread 0.5% quantile over all Monte Carlo simulations

ES_Q025

Extreme spread 2.5% quantile over all Monte Carlo simulations

ES_Q050

Extreme spread 5% quantile over all Monte Carlo simulations

ES_Q100

Extreme spread 10% quantile over all Monte Carlo simulations

ES_Q250

Extreme spread 25% quantile over all Monte Carlo simulations

ES_Q500

Extreme spread 50% quantile (median) over all Monte Carlo simulations

ES_Q750

Extreme spread 75% quantile over all Monte Carlo simulations

ES_Q900

Extreme spread 90% quantile over all Monte Carlo simulations

ES_Q950

Extreme spread 95% quantile over all Monte Carlo simulations

ES_Q975

Extreme spread 97.5% quantile over all Monte Carlo simulations

ES_Q995

Extreme spread 99.5% quantile over all Monte Carlo simulations

FoM_M

Figure of merit mean over all Monte Carlo simulations

FoM_V

Figure of merit variance over all Monte Carlo simulations

FoM_SD

Figure of merit standard deviation over all Monte Carlo simulations

FoM_CV

Figure of merit coefficient of variation over all Monte Carlo simulations

FoM_SKEW

Figure of merit skewness over all Monte Carlo simulations (smoothed)

FoM_KURT

Figure of merit kurtosis over all Monte Carlo simulations (smoothed)

FoM_MED

Figure of merit median (50% quantile) over all Monte Carlo simulations

FoM_Q005

Figure of merit 0.5% quantile over all Monte Carlo simulations

FoM_Q025

Figure of merit 2.5% quantile over all Monte Carlo simulations

FoM_Q050

Figure of merit 0.25% quantile over all Monte Carlo simulations

FoM_Q100

Figure of merit 10% quantile over all Monte Carlo simulations

FoM_Q250

Figure of merit 25% quantile over all Monte Carlo simulations

FoM_Q500

Figure of merit 50% quantile (median) over all Monte Carlo simulations

FoM_Q750

Figure of merit 75% quantile over all Monte Carlo simulations

FoM_Q900

Figure of merit 90% quantile over all Monte Carlo simulations

FoM_Q950

Figure of merit 95% quantile over all Monte Carlo simulations

FoM_Q975

Figure of merit 97.5% quantile over all Monte Carlo simulations

FoM_Q995

Figure of merit 99.5% quantile over all Monte Carlo simulations

D_M

Bounding box diagonal mean over all Monte Carlo simulations

D_V

Bounding box diagonal variance over all Monte Carlo simulations

D_SD

Bounding box diagonal standard deviation over all Monte Carlo simulations

D_CV

Bounding box diagonal coefficient of variation over all Monte Carlo simulations

D_SKEW

Bounding box diagonal skewness over all Monte Carlo simulations (smoothed)

D_KURT

Bounding box diagonal kurtosis over all Monte Carlo simulations (smoothed)

D_MED

Bounding box diagonal median (50% quantile) over all Monte Carlo simulations

D_Q005

Bounding box diagonal 0.5% quantile over all Monte Carlo simulations

D_Q025

Bounding box diagonal 2.5% quantile over all Monte Carlo simulations

D_Q050

Bounding box diagonal 5% quantile over all Monte Carlo simulations

D_Q100

Bounding box diagonal 10% quantile over all Monte Carlo simulations

D_Q250

Bounding box diagonal 25% quantile over all Monte Carlo simulations

D_Q500

Bounding box diagonal 50% quantile (median) over all Monte Carlo simulations

D_Q750

Bounding box diagonal 75% quantile over all Monte Carlo simulations

D_Q900

Bounding box diagonal 90% quantile over all Monte Carlo simulations

D_Q950

Bounding box diagonal 95% quantile over all Monte Carlo simulations

D_Q975

Bounding box diagonal 97.5% quantile over all Monte Carlo simulations

D_Q995

Bounding box diagonal 99.5% quantile over all Monte Carlo simulations

RS_M

Rayleigh sigma mean over all Monte Carlo simulations

RS_V

Rayleigh sigma variance over all Monte Carlo simulations

RS_SD

Rayleigh sigma standard deviation over all Monte Carlo simulations

RS_CV

Rayleigh sigma coefficient of variation over all Monte Carlo simulations

RS_SKEW

Rayleigh sigma skewness over all Monte Carlo simulations (smoothed)

RS_KURT

Rayleigh sigma kurtosis over all Monte Carlo simulations (smoothed)

RS_MED

Rayleigh sigma median (50% quantile) over all Monte Carlo simulations

RS_Q005

Rayleigh sigma 0.5% quantile over all Monte Carlo simulations

RS_Q025

Rayleigh sigma 2.5% quantile over all Monte Carlo simulations

RS_Q050

Rayleigh sigma 5% quantile over all Monte Carlo simulations

RS_Q100

Rayleigh sigma 10% quantile over all Monte Carlo simulations

RS_Q250

Rayleigh sigma 25% quantile over all Monte Carlo simulations

RS_Q500

Rayleigh sigma 50% quantile (median) over all Monte Carlo simulations

RS_Q750

Rayleigh sigma 75% quantile over all Monte Carlo simulations

RS_Q900

Rayleigh sigma 90% quantile over all Monte Carlo simulations

RS_Q950

Rayleigh sigma 95% quantile over all Monte Carlo simulations

RS_Q975

Rayleigh sigma 97.5% quantile over all Monte Carlo simulations

RS_Q995

Rayleigh sigma 99.5% quantile over all Monte Carlo simulations

Details

The Monte Carlo distribution used 10 million repetitions in each scenario. One scenario was a combination of the n shots in each group, and the nGroups groups over which individual range statistics were averaged. Values for n were 2, 3, ..., 49, 50, 45, ..., 95, 100. Values for nGroups were 1, 2, ... 9, 10.

Skewness and kurtosis were smoothed using separate linear spline fits for each number of groups except for kurtosis of Rayleigh sigma which was fitted using the density of the gamma distribution.

Used in range2sigma to estimate Rayleigh parameter sigma from range statistics, and in efficiency to estimate the number of groups and total shots required to estimate the confidence interval (CI) for Rayleigh sigma with a given coverage probability (CI level) and width.

See the following source for an independent simulation, and for the rationale behind using it to estimate Rayleigh sigma:

http://ballistipedia.com/index.php?title=Range_Statistics

An older eqivalent simulation with less repetitions was done by Taylor and Grubbs (1975).

References

Taylor, M. S., & Grubbs, F. E. (1975). Approximate Probability Distributions for the Extreme Spread (BRL-MR-2438). Aberdeen Proving Ground, MD: U.S. Ballistic Research Laboratory.

See Also

range2sigma, efficiency, getMaxPairDist, getBoundingBox, getRayParam

Examples

data(DFdistr)
str(DFdistr)

Description

Example of a combined data frame from several files exported by OnTarget PC/TDS, each with several groups of bullet holes.

Usage

data(DFinch)

Format

A data frame with 487 observations on the following 13 variables.

project.title

a character vector giving the OnTarget PC/TDS project title.

group

a factor with levels 1 2 3. This is the original Group variable as defined by OnTarget PC/TDS.

ammunition

a character vector describing the ammo.

distance

a numerical vector giving the distance to the target.

aim.x

a numerical vector of x-coordinates giving the point of aim.

aim.y

a numerical vector of y-coordinates giving the of point of aim.

center.x

a numerical vector of x-coordinates giving the group centers.

center.y

a numerical vector of y-coordinates giving the group centers.

point.x

a numerical vector of absolute x-coordinates of bullet holes.

point.y

a numerical vector of absolute y-coordinates of bullet holes.

origin

a factor with levels 1 2 3. This factor codes from which original output file the data is.

orgser

a factor with levels 1.1 2.1 3.1 1.2 2.2 3.2 1.3 2.3 3.3. This factor results from droplevels(interaction(origin, group)), and codes each separate group across original files. The order of the factor levels is alphabetical.

series

a factor with levels 1 2 3 4 5 6 7 8 9. This factor codes each separate group as defined by orgser, but more conveniently as a number that runs consecutively across original files.

distance.unit

Measurement unit distance to target

point.unit

Measurement unit (x,y)-coordinates

target

Character string "BDS9" indicating the target face. See targets

Details

Several groups of shooting a 9x19mm pistol at 27yd. The measurement unit for coordinates is inch, for distance yards.
This data frame is like those returned by readDataOT1, readDataOT2, or readDataMisc with option combine=TRUE.

See Also

combineData, analyzeGroup, compareGroups

Examples

data(DFinch)
str(DFinch)

Description

Example of a data frame from one file with one group of bullet holes.

Usage

data(DFlandy01)

Format

A data frame with 530 observations on the following 15 variables.

group

a numerical vector with group numbers 1 to 53.

distance

a numerical vector giving the distance to the target.

aim.x

a numerical vector of x-coordinates giving the point of aim.

aim.y

a numerical vector of y-coordinates giving the of point of aim.

point.x

a numerical vector of absolute x-coordinates of bullet holes.

point.y

a numerical vector of absolute y-coordinates of bullet holes.

ammunition

a character vector giving ammunition and lot number.

velocity

a numerical vector of chronograph readings in ft/s.

control

undocumented.

phase1

undocumented.

phase2

undocumented.

file

a character vector with the original file name.

groupVerb

a character vector designating the group by combining the original file name and ammunition.

series

a character vector that codes each separate group in an alternative way.

seriesNum

like series but numeric.

distance.unit

Measurement unit distance to target

point.unit

Measurement unit (x,y)-coordinates

Details

53 groups with 10 shots each of .22LR shot at Eley test center on Oct 2 2016 using a Stiller 2500X action at a distance of 50m. The measurement unit for coordinates is mm, for distance m.
This data frame is like those returned by readDataOT1, readDataOT2, or readDataMisc with option combine=TRUE.
Data courtesy of Larry Landercasper, 2017. Analyzed by Albert Highe.

See Also

combineData, analyzeGroup, compareGroups

Examples

data(DFlandy01)
str(DFlandy01)

Description

Example of a data frame from one file with one group of bullet holes.

Usage

data(DFlandy02)

Format

A data frame with 100 observations on the following 12 variables.

group

a numerical vector with group numbers 1, 2.

distance

a numerical vector giving the distance to the target.

aim.x

a numerical vector of x-coordinates giving the point of aim.

aim.y

a numerical vector of y-coordinates giving the of point of aim.

point.x

a numerical vector of absolute x-coordinates of bullet holes.

point.y

a numerical vector of absolute y-coordinates of bullet holes.

ammunition

a character vector giving ammunition and lot number.

velocity

a numerical vector of chronograph readings in ft/s.

file

a character vector with the original file name.

groupVerb

a character vector designating the group by combining the original file name and ammunition.

series

a character vector that codes each separate group in an alternative way.

seriesNum

like series but numeric.

distance.unit

Measurement unit distance to target

point.unit

Measurement unit (x,y)-coordinates

Details

2 groups with 50 shots each of .22LR shot using a Stiller 2500X action at a distance of 50yd. The measurement unit for coordinates is inch, for distance yards. Group 1 is from the best of 3 lots, group 2 from worst of 3 lots.
This data frame is like those returned by readDataOT1, readDataOT2, or readDataMisc with option combine=TRUE.
Data courtesy of Larry Landercasper, 2017.

See Also

combineData, analyzeGroup, compareGroups

Examples

data(DFlandy02)
str(DFlandy02)

Description

Example of a data frame from one file with one group of bullet holes.

Usage

data(DFlandy03)

Format

A data frame with 100 observations on the following 12 variables.

group

a numerical vector with group numbers 1, 2.

distance

a numerical vector giving the distance to the target.

aim.x

a numerical vector of x-coordinates giving the point of aim.

aim.y

a numerical vector of y-coordinates giving the of point of aim.

point.x

a numerical vector of absolute x-coordinates of bullet holes.

point.y

a numerical vector of absolute y-coordinates of bullet holes.

ammunition

a character vector giving ammunition and lot number.

velocity

a numerical vector of chronograph readings in ft/s.

file

a character vector with the original file name.

groupVerb

a character vector designating the group by combining the original file name and ammunition.

series

a character vector that codes each separate group in an alternative way.

seriesNum

like series but numeric.

distance.unit

Measurement unit distance to target

point.unit

Measurement unit (x,y)-coordinates

Details

4 groups with 25 shots each of .22LR shot at a distance of 50yd. The measurement unit for coordinates is inch, for distance yards.
Data courtesy of Larry Landercasper, 2017.

See Also

combineData, analyzeGroup, compareGroups

Examples

data(DFlandy03)
str(DFlandy03)

Description

Example of a data frame from one file with one group of bullet holes.

Usage

data(DFlandy04)

Format

A data frame with 100 observations on the following 12 variables.

group

a numerical vector with group numbers 1, 2.

distance

a numerical vector giving the distance to the target.

aim.x

a numerical vector of x-coordinates giving the point of aim.

aim.y

a numerical vector of y-coordinates giving the of point of aim.

point.x

a numerical vector of absolute x-coordinates of bullet holes.

point.y

a numerical vector of absolute y-coordinates of bullet holes.

ammunition

a character vector giving ammunition and lot number.

velocity

a numerical vector of chronograph readings in ft/s.

file

a character vector with the original file name.

groupVerb

a character vector designating the group by combining the original file name and ammunition.

series

a character vector that codes each separate group in an alternative way.

seriesNum

like series but numeric.

distance.unit

Measurement unit distance to target

point.unit

Measurement unit (x,y)-coordinates

Details

6 groups with 25 shots each (groups 1-5) or 50 shots (group 6) of .22LR shot at a distance of 50yd. The measurement unit for coordinates is inch, for distance yards.
Groups 1-3 shot with a Stiller Copperhead action with Shilen Octagon Barrel. Group 4-5 shot with a Baity Falcon action with Shilen Ratchet Barrel. Group 6 shot with a Stiller 2500X action with Shilen Octagon Barrel.
This data frame is like those returned by readDataOT1, readDataOT2, or readDataMisc with option combine=TRUE.
Data courtesy of Larry Landercasper, 2017.

See Also

combineData, analyzeGroup, compareGroups

Examples

data(DFlandy04)
str(DFlandy04)

Description

Example list containing several data frames with bullet hole data as produced by readDataOT1, readDataOT2, or by readDataMisc with option combine=FALSE.

Usage

data(DFlistCm)

Details

Several groups of shooting a 9x19mm pistol at 25m. The measurement unit for coordinates is cm, for distance meters.
This list can be used as an argument for combineData.

See Also

combineData, readDataMisc, readDataOT1, readDataOT2

Examples

data(DFlistCm)
str(DFlistCm)

## combine list of data frames to one single data frame
DFcm <- combineData(DFlistCm)
str(DFcm)

Description

Example of a combined data frame from several original files, each with one group.

Usage

data(DFsavage)

Format

A data frame with 180 observations on the following 10 variables.

point.x

a numerical vector of absolute x-coordinates of bullet holes.

point.y

a numerical vector of absolute y-coordinates of bullet holes.

aim.x

a numerical vector of x-coordinates giving the point of aim.

aim.y

a numerical vector of y-coordinates giving the of point of aim.

distance

a numerical vector giving the distance to the target.

group

a factor with level 1. This is the original Group variable as defined by OnTarget PC/TDS.

bullet

a character vector describing the bullet type.

origin

a factor with levels 1 ... 9. This factor codes from which original output file the data is.

orgser

a factor with levels 1.1 ... 9.1. This factor results from droplevels(interaction(Origin, Group)), and codes each separate group across original files. The order of the factor levels is alphabetical.

series

a factor with levels 1 ... 9. This factor codes each separate group as defined by orgser, but more conveniently as a number that runs consecutively across original files.

distance.unit

Measurement unit distance to target

point.unit

Measurement unit (x,y)-coordinates

Details

Several groups of shooting a Savage 12 FT/R rifle in .308 Win at distances from 100 to 300m. The measurement unit for coordinates is mm, for distance meters. Shots 1-5 in series 4, and shots 1-3 in series 7 moved the scope.
This data frame is like those returned by readDataOT1, readDataOT2, or readDataMisc with option combine=TRUE.
Data copyright Charles McMillan and Paul McMillan, 2008.

See Also

combineData, analyzeGroup, compareGroups

Examples

data(DFsavage)
str(DFsavage)

Description

Example of a data frame from one file with one group of bullet holes.

Usage

data(DFscar17)

Format

A data frame with 10 observations on the following 9 variables.

group

a factor with level 1.

distance

a numerical vector giving the distance to the target.

aim.x

a numerical vector of x-coordinates giving the point of aim.

aim.y

a numerical vector of y-coordinates giving the of point of aim.

point.x

a numerical vector of absolute x-coordinates of bullet holes.

point.y

a numerical vector of absolute y-coordinates of bullet holes.

origin

a factor with level 1. This factor codes from which original output file the data is.

orgser

a factor with level 1.1. This factor results from droplevels(interaction(origin, group)), and codes each separate group across original files. The order of the factor levels is alphabetical.

series

a factor with levels 1. This factor codes each separate group as defined by orgser, but more conveniently as a number that runs consecutively across original files.

distance.unit

Measurement unit distance to target

point.unit

Measurement unit (x,y)-coordinates

Details

One group of shooting an FN SCAR 17 rifle in .308 Win at 100yd. The measurement unit for coordinates is inch, for distance yards.
This data frame is like those returned by readDataOT1, readDataOT2, or readDataMisc with option combine=TRUE.
Data courtesy of David Bookstaber, 2013. http://ballistipedia.com/

See Also

combineData, analyzeGroup, compareGroups

Examples

data(DFscar17)
str(DFscar17)

Description

Example of a combined data frame from several original files, each file containing one group.

Usage

data(DFtalon)

Format

A data frame with 180 observations on the following 10 variables.

point.x

a numerical vector of absolute x-coordinates of bullet holes.

point.y

a numerical vector of absolute y-coordinates of bullet holes.

aim.x

a numerical vector of x-coordinates giving the point of aim.

aim.y

a numerical vector of y-coordinates giving the of point of aim.

distance

a numerical vector giving the distance to the target.

group

a factor with level 1. This is the original Group variable as defined by OnTarget PC/TDS.

bullet

a character vector describing the bullet type.

origin

a factor with levels 1 ... 9. This factor codes from which original output file the data is.

orgser

a factor with levels 1.1 ... 9.1. This factor results from droplevels(interaction(Origin, Group)), and codes each separate group across original files. The order of the factor levels is alphabetical.

series

a factor with levels 1 ... 9. This factor codes each separate group as defined by orgser, but more conveniently as a number that runs consecutively across original files.

distance.unit

Measurement unit distance to target

point.unit

Measurement unit (x,y)-coordinates

Details

Several groups of shooting a Talon SS air rifle at 10m. The measurement unit for coordinates is mm, for distance meters.
This data frame is like those returned by readDataOT1, readDataOT2, or readDataMisc with option combine=TRUE.
Data copyright Charles McMillan and Paul McMillan, 2008.

See Also

combineData, analyzeGroup, compareGroups

Examples

data(DFtalon)
str(DFtalon)

Description

Adds an axis-aligned box to an existing plot.

Usage

drawBox(x, fg = par('fg'), bg = NA,
        colCtr = NA, lty = par('lty'), lwd = par('lwd'),
        pch = par('pch'), cex = par('cex'))

## S3 method for class 'list'
drawBox(x, fg = par('fg'), bg = NA,
        colCtr = NA, lty = par('lty'), lwd = par('lwd'),
        pch = par('pch'), cex = par('cex'))

## Default S3 method:
drawBox(x, fg = par('fg'), bg = NA,
        colCtr = NA, lty = par('lty'), lwd = par('lwd'),
        pch = par('pch'), cex = par('cex'))

Arguments

Details

This function is mainly a wrapper for rect.

See Also

getBoundingBox, rect

Examples

xy  <- matrix(round(rnorm(20, 100, 15), 1), ncol=2)
(bb <- getBoundingBox(xy))

plot(xy, asp=1, pch=16)
drawBox(bb, fg='blue', colCtr='blue', pch=4, cex=2)

Description

Adds an oriented box to an existing plot.

Usage

drawBox2(x, fg = par('fg'), bg = NA, colCtr = NA,
         lty = par('lty'), lwd = par('lwd'), pch = par('pch'),
         cex = par('cex'))

## S3 method for class 'list'
drawBox2(x, fg = par('fg'), bg = NA, colCtr = NA,
         lty = par('lty'), lwd = par('lwd'), pch = par('pch'),
         cex = par('cex'))

## Default S3 method:
drawBox2(x, fg = par('fg'), bg = NA, colCtr = NA,
         lty = par('lty'), lwd = par('lwd'), pch = par('pch'),
         cex = par('cex'))

Arguments

Details

This function is mainly a wrapper for polygon.

See Also

getMinBBox, polygon

Examples

xy  <- matrix(round(rnorm(20, 100, 15), 1), ncol=2)
(bb <- getMinBBox(xy))

plot(xy, xlim=range(c(xy[ , 1], bb$pts[ , 1])),
         ylim=range(c(xy[ , 2], bb$pts[ , 2])), asp=1, pch=16)
drawBox2(bb, fg='blue', colCtr='blue', pch=4, cex=2)

Description

Adds a circle to an existing plot.

Usage

drawCircle(x, radius, nv = 100, fg = par('fg'), bg = NA,
           colCtr = NA, lty = par('lty'), lwd = par('lwd'),
           pch = par('pch'), cex = par('cex'))

## S3 method for class 'list'
drawCircle(x, radius, nv = 100, fg = par('fg'), bg = NA,
           colCtr = NA, lty = par('lty'), lwd = par('lwd'),
           pch = par('pch'), cex = par('cex'))

## Default S3 method:
drawCircle(x, radius, nv = 100, fg = par('fg'), bg = NA,
           colCtr = NA, lty = par('lty'), lwd = par('lwd'),
           pch = par('pch'), cex = par('cex'))

Arguments

Details

This function is mainly a wrapper for polygon. To draw more than a few circles efficiently, use symbols instead.

See Also

polygon, symbols, getMinCircle

Examples

c1 <- c(1, 2)                 # circle center
c2 <- c(2, 3)                 # another circle center
r1 <- 2                       # circle radius
r2 <- 0.5                     # another circle radius

# determine axis limits so that circles will be visible
xLims <- c1[1] + c(-r1, r1)
yLims <- c1[2] + c(-r1, r1)

plot(c1[1], c1[2], type='n', asp=1, xlim=xLims, ylim=yLims)
drawCircle(c1, r1, fg='blue', colCtr='blue', pch=19)
drawCircle(c2, r2, fg='red', bg='red', colCtr='black', pch=4)

Description

Adds an ellipse to an existing plot.

Usage

drawEllipse(x, shape, radius, nv = 100, axes = FALSE,
            fg = par('fg'), bg = NA, colCtr = NA, lty = par('lty'),
            lwd = par('lwd'), pch = par('pch'), cex = par('cex'))

## S3 method for class 'list'
drawEllipse(x, shape, radius, nv = 100, axes = FALSE,
            fg = par('fg'), bg = NA, colCtr = NA, lty = par('lty'),
            lwd = par('lwd'), pch = par('pch'), cex = par('cex'))

## Default S3 method:
drawEllipse(x, shape, radius, nv = 100, axes = FALSE,
            fg = par('fg'), bg = NA, colCtr = NA, lty = par('lty'),
            lwd = par('lwd'), pch = par('pch'), cex = par('cex'))

Arguments

Details

This function is mainly a wrapper for polygon.

See Also

polygon, getConfEll, getMinEllipse

Examples

## error ellipse for a set of points
xy <- matrix(round(rnorm(100, 0, 8), 2), ncol=2)
ce <- getConfEll(xy)
plot(xy, pch=16, asp=1)
drawEllipse(ce, radius=1, axes=TRUE, fg='blue', colCtr='blue',
            lwd=2, pch=4, cex=2)

Description

Draws a group with scaled bullet holes on a target background. Spread measures can be selected individually.

Usage

drawGroup(xy, center = FALSE, xyTopLeft = TRUE,
          bb = FALSE, bbMin = FALSE, bbDiag = FALSE,
          minCirc = FALSE, minEll = FALSE, maxSpread = FALSE,
          meanDist = FALSE, confEll = FALSE,
          CEP = FALSE, ringID = FALSE, valueID = TRUE, doRob = FALSE,
          level = 0.95, scaled = TRUE, caliber = 9, dstTarget, conversion,
          unit = 'unit', alpha = 0.5, target)

## S3 method for class 'data.frame'
drawGroup(xy, center = FALSE, xyTopLeft = TRUE,
          bb = FALSE, bbMin = FALSE, bbDiag = FALSE,
          minCirc = FALSE, minEll = FALSE,
          maxSpread = FALSE, meanDist = FALSE, confEll = FALSE,
          CEP = FALSE, ringID = FALSE, valueID = TRUE, doRob = FALSE,
          level = 0.95, scaled = TRUE, caliber = 9, dstTarget, conversion,
          unit = 'unit', alpha = 0.5, target)

## Default S3 method:
drawGroup(xy, center = FALSE, xyTopLeft = TRUE,
          bb = FALSE, bbMin = FALSE, bbDiag = FALSE,
          minCirc = FALSE, minEll = FALSE,
          maxSpread = FALSE, meanDist = FALSE, confEll = FALSE,
          CEP = FALSE, ringID = FALSE, valueID = TRUE, doRob = FALSE,
          level = 0.95, scaled = TRUE, caliber = 9, dstTarget, conversion,
          unit = 'unit', alpha = 0.5, target)

Arguments

Value

Invisibly returns a list with the following components, all converted to unit (if they were requested):

See Also

getBoundingBox, getMinBBox, getMinCircle, getMinEllipse, getMaxPairDist, getDistToCtr, getConfEll, drawBox, drawBox2, drawCircle, drawEllipse, targets, drawTarget, simRingCount, covMcd

Examples

# draw group in MOA
dg <- drawGroup(DFcciHV, xyTopLeft=TRUE, bb=TRUE, minCirc=TRUE,
                confEll=TRUE, maxSpread=TRUE, caliber=5.56, unit='MOA',
                dstTarget=100, conversion='yd2in', target='BDS9')

# mininum enclosing circle in MOA
dg$minCirc

# show Grubbs-Patnaik CEP estimator for mulitple levels
drawGroup(DF300BLKhl, CEP="GrubbsPatnaik", level=c(0.5, 0.9, 0.95),
          dstTarget=100, conversion="yd2in", caliber=7.62)

Description

Draws a target pattern - either from the name of a pre-specified target type or from a supplied list defining the target.

Usage

drawTarget(x, unit, dstTarget, conversion,
           add = FALSE, cex = par('cex'))

Arguments

Value

Invisibly returns a list with (at least) the following components defining the target:

See Also

targets, drawGroup

Examples

# draw ISSF 300m target in inch
trgt <- drawTarget('ISSF_300m', unit='in')

# target definition
trgt

Description

Estimates the approximate number of required groups for a given number of shots per group, confidence interval (CI) level and CI width - when using the Rayleigh sigma estimator based on (x,y)-coordinates, or a range statistic such as extreme spread, figure of merit, or the bounding box diagonal. The function may also be used to obtain the estimated CI width when the number of shots per group and the number of groups is given. This functions assumes a circular bivariate normal shot distribution with 0 mean.

Usage

efficiency(n, nGroups, CIlevel=0.95, CIwidth,
           stat=c("Rayleigh", "ES", "FoM", "D"))

Arguments

Details

Based on the lookup table DFdistr with results form a Monte Carlo simulation. If the value of n is not among those simulated (but is less than 100), a spline interpolation between the neighboring simulated values of the statistic's coefficient of variation is used.

The number of required groups is approximate as the calculation assumes a normal distribution for the mean statistic. Details for the calculation can be found under

http://ballistipedia.com/index.php?title=Range_Statistics

http://www.geoffrey-kolbe.com/articles/rimfire_accuracy/group_statistics.htm

http://ballistipedia.com/images/3/32/Sitton_1990.pdf

If package shiny is installed, an interactive web app for this functionality can be run with runGUI("range").

Value

When CIwidth is given, a data frame with the estimated number of required groups and total shots to achieve the given CIlevel.

When nGroups is given, a data frame with the estimated CI width required to achieve the desired CIlevel.

See Also

DFdistr, range2sigma, getRayParam, getMaxPairDist, getBoundingBox

Examples

# get required number of shots to achieve 90% CI with
# a CI width of 20% of the mean (10% on either side)
# using 10 shots per group and measuring extreme spread
efficiency(n=10, CIlevel=0.9, CIwidth=0.2, stat="ES")

# as above, but using Rayleigh sigma
efficiency(n=10, CIlevel=0.9, CIwidth=0.2, stat="Rayleigh")

# check that the result for ES is about right
# -> 5% quantile with 10 groups is about 10% below the mean
# -> 95% quantile with 10 groups is about 10% above the mean
with(subset(DFdistr, (n == 10L) & (nGroups == 10L)),
     c(ES_Q050/ES_M, ES_Q950/ES_M))

# get achievable 90% CI width with 10 groups of 5 shots each
# using extreme spread
efficiency(n=5, nGroups=10, CIlevel=0.9, stat="ES")

Description

Converts angular diameter (degree, radian, minute of angle MOA = arcminute, Shooter's MOA SMOA, milliradian mrad, NATO mil) to object size.

Usage

fromMOA(x, dst, conversion,
        type = c('deg', 'rad', 'MOA', 'SMOA', 'mrad', 'mil'))

Arguments

Details

1 MOA (minute of angle, arcmin) = 1/60 degree. Shooter's MOA = SMOA = Inches Per Hundred Yards IPHY. 1 inch at 100 yards = 1 SMOA. 1 milliradian = 1/1000 radian. 1 mil = 2*pi/6400 radian (NATO definition: the circle circumference is divided into 6400 mils). Details are given in the vignette, see vignette('shotGroups') .

If package shiny is installed, an interactive web app for this functionality can be run with runGUI("angular").

Value

A numerical vector with the object sizes. The measurement unit is determined by conversion.

See Also

getMOA, getDistance

Examples

size <- seq(1, 20, by=5)   # inch
dst  <- 100                # yard
fromMOA(size, dst=dst, conversion='yd2in', type='MOA')

# this should return objSize
MOA <- getMOA(size, dst=dst, conversion='yd2in', type='MOA')
fromMOA(MOA, dst=dst, conversion='yd2in', type='MOA')
        
# SMOA
fromMOA(c(1, 2, 5), dst=100, conversion='yd2in', type='SMOA')

# milliradian
fromMOA(c(1, 2, 5), dst=100, conversion='m2mm', type='mrad')

Description

Calculates the vertices of the (axis-parallel) bounding box given a set of 2D-coordinates.

Usage

getBoundingBox(xy)

## S3 method for class 'data.frame'
getBoundingBox(xy)

## Default S3 method:
getBoundingBox(xy)

Arguments

Details

No coordinate transforms are done (unlike in groupLocation, groupShape, groupSpread), i.e., origin is not assumed to be in top-left corner, and points are not taken relative to point of aim.

Value

A list with the following information about the bounding box:

See Also

drawBox, getMinBBox, getMinCircle

Examples

# coordinates given by a suitable data frame
bb <- getBoundingBox(DFsavage)

# draw points and bounding box
plot(point.y ~ point.x, data=DFsavage, asp=1, pch=16)
drawBox(bb, fg='blue', colCtr='blue', pch=4, cex=2)

bb$FoM                                   # figure of merit

# coordinates given by a matrix
## Not run: 
xy <- matrix(round(rnorm(20, 100, 15), 1), ncol=2)
getBoundingBox(xy)

## End(Not run)

Description

Estimates the Circular Error Probable (CEP) or the Spherical Error Probable (SEP). CEP/SEP is defined as the radius of the circle/sphere around the point of aim such that it contains a certain fraction of points of impact, e.g., 50% or 90%.

Usage

getCEP(xy, CEPlevel=0.5, dstTarget, conversion,
       center = FALSE, accuracy = FALSE, type = 'CorrNormal', doRob = FALSE)

## S3 method for class 'data.frame'
getCEP(xy, CEPlevel=0.5, dstTarget, conversion,
       center = FALSE, accuracy = FALSE, type = 'CorrNormal', doRob = FALSE)

## Default S3 method:
getCEP(xy, CEPlevel=0.5, dstTarget, conversion,
       center = FALSE, accuracy = FALSE, type = 'CorrNormal', doRob = FALSE)

Arguments

Details

For accuracy=FALSE (default), the reported CEP/SEP estimates do not take into account accuracy, i.e., any systematic location bias. The data is then first centered on the empirical group mean, assumed to coincide with the point of aim. The resulting CEP/SEP-MPI (around Mean Point of Impact) is a pure precision (spread) measure. Set accuracy=TRUE to incorporate systematic accuracy bias such that the point of aim is in the origin 0, possibly offset from the true group center.

• CorrNormal: For accuracy=FALSE and two-dimensional data, this estimate is based on the correlated bivariate normal distribution re-written in polar coordinates (radius and angle) (see Hoyt). For accuracy=TRUE or three-dimensional data, it is based on the (offset) circle/sphere probabilities for the correlated multivariate normal distribution (DiDonato & Jarnagin, 1961; DiDonato, 1981, see qmvnEll). This estimate is available for all probability levels.

• GrubbsPearson: The Grubbs-Pearson estimate (Grubbs, 1964) is based on the Pearson three-moment central chi^2-approximation of the true cumulative distribution function of radial error. The eigenvalues of the covariance matrix of shot-coordinates are used as variance estimates since they are the variances of the principal components (the PCA-rotated = decorrelated data). This estimate is available for all probability levels, and generalizes to three dimensions.

• GrubbsPatnaik: The Grubbs-Patnaik estimate (Grubbs, 1964) differs from the Grubbs-Pearson estimate insofar as it is based on the Patnaik two-moment central chi^2-approximation of the true cumulative distribution function of radial error.

• GrubbsLiu: The Grubbs-Liu estimate was not proposed by Grubbs but follows the same principle as his original estimates. It differs from them insofar as it is based on the Liu-Tang-Zhang four-moment non-central chi^2-approximation of the true cumulative distribution function of radial error. For accuracy=FALSE, it is identical to GrubbsPearson.

• Rayleigh: For accuracy=FALSE and two-dimensional data, this estimate uses the Rayleigh distribution (see getRayParam). It is valid for uncorrelated bivariate normal coordinates with equal variances. This estimate is available for all probability levels. For accuracy=FALSE and three-dimensional data, the Maxwell-Boltzmann distribution is used (see getRayParam). For accuracy=TRUE and two-dimensional data, the estimate uses the Rice distribution (see getRiceParam). For accuracy=TRUE and three-dimensional data, it is based on the offset sphere probabilities for the multivariate normal distribution set to have equal variances (see qmvnEll).

• Krempasky: The Krempasky estimate (Krempasky, 2003) is based on a nearly exact closed-form solution for the 50% quantile of the radial error for the correlated bivariate normal distribution with 0 mean. It requires estimating the covariance matrix and can only be reported for probability 0.5 with accuracy=FALSE. It does not generalize to three dimensions.

• Ignani: The Ignani estimate (Ignani, 2010) is based on a polynomial approximation for some quantiles of the radial error for the correlated bivariate normal distribution with 0 mean. It requires estimating the covariance matrix and can only be reported for probabilities 0.5, 0.9, 0.95, 0.99 with accuracy=FALSE. It generalizes to three dimensions.

• RMSE: For accuracy=FALSE, this estimator is the RMSE estimator often described in the GPS literature (van Diggelen, 2007) when using centered data for calculating RMSE (square root of the mean squared error). It is very similar to the Rayleigh estimator. For accuracy=TRUE, this the RMSE estimator often described in the GPS literature when using the original, non-centered data for calculating RMSE. It is similar to the Rayleigh estimator only when bias is small, but becomes seriously wrong otherwise. It is available for all probability levels, and generalizes to three dimensions.

• Ethridge: The Ethridge estimate (Ethridge, 1983; Puhek, 1992) is not based on the assumption of multivariate normality of coordinates but uses a robust unbiased estimator for the median radius (Hogg, 1967). It can only be reported for probability 0.5 but generalizes to three dimensions.

• RAND: The modified RAND R-234 estimate (RAND, 1952; Pesapane & Irvine, 1977; Puhek 1992) is a weighted sum of the square root of the eigenvalues of the covariance matrix of shot coordinates (the standard deviations of the data that is first de-correlated through rotation). It can only be reported for probability 0.5 and does not generalize to three dimensions.

• Valstar: Very similar to the RAND R-234 estimate with accuracy=FALSE except for very elliptical distributions but with a different bias correction with accuracy=TRUE. It can only be reported for probability 0.5 and does not generalize to three dimensions.

Estimators based on the normal distribution use the plug-in method (Blischke & Halpin, 1966), i.e., they substitute the true covariance matrix and mean vector with those estimated from the data. They are thus strictly valid only for the asymptotic distribution, while the finite sample distribution may differ somewhat.

If package shiny is installed, an interactive web app for this functionality can be run with runGUI("hitprob").

Value

A list with the (chosen) CEP/SEP estimates and supplementary information on the distribution shape.

References

Blischke W. R. and Halpin, A. H. (1966). Asymptotic properties of some estimators of quantiles of circular error. Journal of the American Statistical Association, 61 (315), 618-632.

DiDonato, A. R. (1988). Integration of the trivariate normal distribution over an offset spehere and an inverse problem (NSWC TR 87-27). Dahlgren, VA: U.S. Naval Surface Weapons Center Dahlgren Division.

DiDonato, A. R., & Jarnagin, M. P. (1961). Integration of the general bivariate Gaussian distribution over an offset circle. Mathematics of Computation, 15 (76), 375-382.

Grubbs, F. E. (1964). Approximate circular and noncircular offset probabilities of hitting. Operations Research, 12(1), 51-62.

Hogg, R. V. (1967). Some observations on robust estimation. Journal of the American Statistical Association, 62 (320), 1179-1186.

Ignani, B. (2010). Determination of Circular and Spherical Position-Error Bounds in System Performance Analysis. Journal of Guidance, Control, and Dynamics, 33 (4), 1301-1304.

Krempasky, J. J. (2003). CEP equation exact to the fourth order. Navigation: Journal of The Institute of Navigation, 50 (3), 143-149.

Liu, H., Tang, Y., & Zhang, H. H. (2009). A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables. Computational Statistics & Data Analysis, 53(4), 853-856.

Pesapane, J., & Irvine, R. B. (1977). Derivation of CEP formula to approximate RAND-234 tables. Offut AFB, NE: Ballistic Missile Evaluation, HQ SAC.

Puhek, P. (1992). Sensitivity analysis of circular error probable approximation techniques (AFIT/GOR/ENS/92M-23). Wright-Patterson AFB, OH: Air Force Institute of Technology.

RAND Corporation. (1952). Offset circle probabilities (RAND-234). Santa Monica, CA: RAND Corporation.

Singh, H. P. 1992. Estimation of Circular Probable Error. The Indian Journal of Statistics, Series B 5(3), 289-305.

van Diggelen, F. 2007. Update: GNSS Accuracy: Lies, Damn Lies, and Statistics. GPS World.

See Also

Rayleigh, Maxwell, Hoyt, Rice, mvnEll, getHoytParam, getRayParam, getRiceParam, getConfEll, getHitProb, covMcd

Examples

# coordinates given by a suitable data frame
(cep <- getCEP(DFtalon, CEPlevel=0.5, accuracy=FALSE,
               dstTarget=10, conversion='m2mm',
               type=c('CorrNormal', 'GrubbsPatnaik', 'Rayleigh')))

# plot points, centers, and circles indicating 50%-CEP estimates
plot(point.y ~ point.x, data=DFtalon, asp=1, pch=16)
drawCircle(cep$ctr, cep$CEP$CEP0.5['unit', 'CorrNormal'],    fg='red')
drawCircle(cep$ctr, cep$CEP$CEP0.5['unit', 'GrubbsPatnaik'], fg='green3')
drawCircle(cep$ctr, cep$CEP$CEP0.5['unit', 'Rayleigh'],      fg='blue')
points(cep$ctr[1], cep$ctr[2], pch=4, col='gray50', cex=2, lwd=2)
legend(x='bottomleft',
       legend=c('Grubbs 50', 'Corr Normal 50', 'Rayleigh 50', 'center'),
       col=c('red', 'green3', 'blue', 'gray50'), lwd=2,
       lty=c(1, 1, 1, NA), pch=c(NA, NA, NA, 4), bg='white')

# calculate actual coverage percentage of 50% CEP estimates
dists <- getDistToCtr(DFtalon)           # distances to center

# extract CEP radius for all estimates
CEPr <- cep$CEP$CEP0.5['unit', ]

# percentage of points in circle with radius = CEP
100 * sapply(CEPr, function(x) sum(dists <= x)) / length(dists)

# coordinates given by a matrix
## Not run: 
xy <- matrix(round(rnorm(100, 0, 5), 2), ncol=2)
getCEP(xy, accuracy=FALSE, dstTarget=25, conversion='m2cm',
       type=c('Grubbs', 'CorrNormal', 'Rayleigh'))

## End(Not run)

Description

Calculates the confidence ellipse for the true mean of shot coordinates under the assumption of multivariate normality. Also includes the ellipse based on a robust estimate for the covariance matrix of the shot coordinates.

Usage

getConfEll(xy, level = 0.5, dstTarget, conversion,
          center = FALSE, doRob=TRUE)

## S3 method for class 'data.frame'
getConfEll(xy, level = 0.5, dstTarget, conversion,
          center = FALSE, doRob=TRUE)

## Default S3 method:
getConfEll(xy, level = 0.5, dstTarget, conversion,
          center = FALSE, doRob=TRUE)

Arguments

Details

No coordinate transforms are done (unlike in groupLocation, groupShape, groupSpread), i.e., origin is not assumed to be in top-left corner, and points are not taken relative to point of aim.

Robust estimate for the covariance matrix of coordinates is from covMcd using the MCD algorithm. See getCEP for estimates of the circular/spherical error probable.

Value

A list with the confidence ellipse measures.

See Also

getCEP, covMcd, drawEllipse

Examples

# coordinates given by a suitable data frame
(ce <- getConfEll(DFsavage, level=0.5, dstTarget=100,
                  conversion='yd2in'))

# plot points, center, parametric confidence
# ellipse, and its axes
plot(point.y ~ point.x, data=DFsavage, asp=1, pch=16)
drawEllipse(ce, axes=TRUE, fg='blue', colCtr='blue', lwd=2, pch=4, cex=2)

# coordinates given by a matrix
## Not run: 
xy <- matrix(round(rnorm(100, 0, 5), 2), ncol=2)
getConfEll(xy, level=0.5, dstTarget=25, conversion='m2cm')

## End(Not run)

Description

Calculates the distance to an object based on the object's absolute and angular size.

Usage

getDistance(x, angular, conversion,
            type = c('deg', 'rad', 'MOA', 'SMOA', 'mrad', 'mil'))

Arguments

Details

1 MOA (minute of angle, arcmin) = 1/60 degree. Shooter's MOA = SMOA = Inches Per Hundred Yards IPHY. 1 inch at 100 yards = 1 SMOA. 1 milliradian = 1/1000 radian. 1 mil = 2*pi/6400 radian (NATO definition: the circle circumference is divided into 6400 mils). Details are given in the vignette, see vignette('shotGroups')

Value

A numerical vector with the distance values.

See Also

getMOA, fromMOA

Examples

size <- seq(1, 20, by=5)   # inch
dst  <- 100                # yard

# get angular size in MOA from absolute size
angular <- getMOA(size, dst=dst, conversion='yd2in', type='MOA')

# this should return dst throughout
getDistance(size, angular=angular, conversion='yd2in', type='MOA')

Description

Calculates the distances of a set of points to their center.

Usage

getDistToCtr(xy)

## S3 method for class 'data.frame'
getDistToCtr(xy)

## Default S3 method:
getDistToCtr(xy)

Arguments

Value

A numerical vector with the distances from each point to the center of the set.

Examples

# coordinates given by a suitable data frame
getDistToCtr(DFtalon)

# coordinates given by a matrix
## Not run: 
xy <- matrix(round(rnorm(20, 100, 15), 1), ncol=2)
getDistToCtr(xy)

## End(Not run)

Description

Calculates the hit probability within a circular or spherical region for a given group of two- or three-dimensional coordinates.

Usage

getHitProb(xy, r=1, unit = 'unit', dstTarget, conversion,
           center = FALSE, accuracy = FALSE, type = 'CorrNormal', doRob = FALSE)

## S3 method for class 'data.frame'
getHitProb(xy, r=1, unit = 'unit', dstTarget, conversion,
           center = FALSE, accuracy = FALSE, type = 'CorrNormal', doRob = FALSE)

## Default S3 method:
getHitProb(xy, r=1, unit = 'unit', dstTarget, conversion,
           center = FALSE, accuracy = FALSE, type = 'CorrNormal', doRob = FALSE)

Arguments

Details

The estimated hit probability is the same as the estimated fraction of shots with a distance to their group center of at most r.

For accuracy=FALSE (default), the estimated hit probability does not take into account accuracy, i.e., any systematic location bias. The data is then first centered on the empirical group mean, assumed to coincide with the point of aim. Set accuracy=TRUE to incorporate systematic accuracy bias such that the point of aim is in the origin 0, possibly offset from the true group center.

• CorrNormal: For accuracy=FALSE and two-dimensional data, this estimate is based on the quantile function of the correlated bivariate normal distribution re-written in polar coordinates (radius and angle) (see Hoyt). For accuracy=TRUE or three-dimensional data, it is based on the (offset) circle/sphere probabilities for the correlated multivariate normal distribution (DiDonato & Jarnagin, 1961; DiDonato, 1981, see pmvnEll).

• GrubbsPearson: The Grubbs-Pearson estimate (Grubbs, 1964) is based on the Pearson three-moment central chi^2-approximation of the true cumulative distribution function of radial error. The eigenvalues of the covariance matrix of shot-coordinates are used as variance estimates since they are the variances of the principal components (the PCA-rotated = decorrelated data).

• GrubbsPatnaik: The Grubbs-Patnaik estimate (Grubbs, 1964) differs from the Grubbs-Pearson estimate insofar as it is based on the Patnaik two-moment central chi^2-approximation of the true cumulative distribution function of radial error.

• GrubbsLiu: The Grubbs-Liu estimate was not proposed by Grubbs but follows the same principle as his original estimates. It differs from them insofar as it is based on the Liu-Tang-Zhang four-moment non-central chi^2-approximation of the true cumulative distribution function of radial error. For accuracy=FALSE, it is identical to GrubbsPearson.

• Rayleigh: For accuracy=FALSE and two-dimensional data, this estimate uses the Rayleigh distribution (see getRayParam). It is valid for uncorrelated bivariate normal coordinates with equal variances. This estimate is available for all probability levels. For accuracy=FALSE and three-dimensional data, the Maxwell-Boltzmann distribution is used (see getRayParam). For accuracy=TRUE and two-dimensional data, the estimate uses the Rice distribution (see getRiceParam). For accuracy=TRUE and three-dimensional data, it is based on the offset sphere probabilities for the multivariate normal distribution set to have equal variances (see qmvnEll).

If package shiny is installed, an interactive web app for this functionality can be run with runGUI("hitprob").

Value

A vector with the (chosen) hit-probability estimates. For more than one r and more than one type, a matrix.

References

DiDonato, A. R. (1988). Integration of the trivariate normal distribution over an offset spehere and an inverse problem (NSWC TR 87-27). Dahlgren, VA: U.S. Naval Surface Weapons Center Dahlgren Division.

DiDonato, A. R., & Jarnagin, M. P. (1961). Integration of the general bivariate Gaussian distribution over an offset circle. Mathematics of Computation, 15 (76), 375-382.

Grubbs, F. E. (1964). Approximate circular and noncircular offset probabilities of hitting. Operations Research, 12(1), 51-62.

Liu, H., Tang, Y., & Zhang, H. H. (2009). A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables. Computational Statistics & Data Analysis, 53(4), 853-856.

Singh, H. P. 1992. Estimation of Circular Probable Error. The Indian Journal of Statistics, Series B 5(3), 289-305.

See Also

Rayleigh, Maxwell, Hoyt, mvnEll, getHoytParam, getRayParam, getCEP, getConfEll, covMcd

Examples

# coordinates given by a suitable data frame
# estimated fraction of shots within a circle with radius
# 1 and 1.5 MOA.
getHitProb(DFscar17, r=c(1, 1.5), unit='MOA', accuracy=FALSE,
           dstTarget=100, conversion='yd2in',
           type=c('CorrNormal', 'GrubbsPatnaik'))

# coordinates given by a matrix
## Not run: 
xy <- matrix(round(rnorm(100, 0, 5), 2), ncol=2)
getHitProb(xy, r=c(2, 2.5), unit='MOA', accuracy=FALSE,
           dstTarget=100, conversion='yd2in',
           type=c('CorrNormal', 'GrubbsPatnaik'))

## End(Not run)

Description

Determines the Hoyt distribution's shape parameter q and scale parameter omega from the eigenvalues of a (2 x 2)-covariance matrix.

Usage

getHoytParam(x)

## S3 method for class 'matrix'
getHoytParam(x)

## S3 method for class 'list'
getHoytParam(x)

## S3 method for class 'data.frame'
getHoytParam(x)

## Default S3 method:
getHoytParam(x)

Arguments

Details

The parameters q and omega derive from the eigenvalues ev1, ev2 of the covariance matrix of the bivariate normal distribution as follows: q = 1 / sqrt(((ev1+ev2)/ev2) - 1) and omega = ev1 + ev2.

If x is a data frame, its sample covariance matrix is used to estimate the eigenvalues. Note that the Hoyt distribution is only approximately valid for large samples if estimated parameters are used.

Value

A list with the following components:

References

Hoyt, R. S. (1947). Probability functions for the modulus and angle of the normal complex variate. Bell System Technical Journal, 26(2), 318-359.

https://reference.wolfram.com/language/ref/HoytDistribution.html

See Also

Hoyt

Examples

## q and omega based on coordinates in a data frame
getHoytParam(DFscar17)

## q and omega based on a covariance matrix
cm1 <- cbind(c(8, 0), c(0, 2))
getHoytParam(cm1)

## q and omega based on a list of covariance matrices
cm2 <- cbind(c(6, 0), c(0, 4))
cmL <- list(cm1, cm2)
getHoytParam(cmL)

## q and omega based on eigenvalues
ev <- eigen(cm1)$values
getHoytParam(cm1)

Description

Estimates the Kuchnost precision measure. The maximum distance to the group center after removing outliers.

Usage

getKuchnost(xy, dstTarget, conversion,
       center = FALSE, doRob = FALSE, strict = FALSE)

## S3 method for class 'data.frame'
getKuchnost(xy, dstTarget, conversion,
       center = FALSE, doRob = FALSE, strict = FALSE)

## Default S3 method:
getKuchnost(xy, dstTarget, conversion,
       center = FALSE, doRob = FALSE, strict = FALSE)

Arguments

Details

An outlier is defined as a shot that is at least 2.5 times further away from the group center defined by all remaining shots compared to the maximum distance to center of those shots themselves.

Value

A list with 3 components.

References

https://github.com/lstange/mcgs

See Also

covMcd

Examples

getKuchnost(DF300BLK)

Description

Calculates the maximum of pairwise distances between points given a set of coordinates.

Usage

getMaxPairDist(xy)

## S3 method for class 'data.frame'
getMaxPairDist(xy)

## Default S3 method:
getMaxPairDist(xy)

Arguments

Value

A list with the following components

Examples

# coordinates given by a suitable data frame
(maxPD <- getMaxPairDist(DFsavage))

# plot points and point pair with maximum distance
plot(point.y ~ point.x, data=DFsavage, asp=1, pch=16)
x0 <- DFsavage$point.x[maxPD$idx[1]]     # 1st point x
y0 <- DFsavage$point.y[maxPD$idx[1]]     # 1st point y
x1 <- DFsavage$point.x[maxPD$idx[2]]     # 2nd point x
y1 <- DFsavage$point.y[maxPD$idx[2]]     # 2nd point y
segments(x0, y0, x1, y1, col="green3", lwd=2)

# coordinates given by a matrix
## Not run: 
xy <- matrix(round(rnorm(20, 100, 15), 1), ncol=2)
getMaxPairDist(xy)

## End(Not run)

Description

Calculates the vertices of the minimum-area, possibly oriented bounding box given a set of 2D-coordinates.

Usage

getMinBBox(xy)

## S3 method for class 'data.frame'
getMinBBox(xy)

## Default S3 method:
getMinBBox(xy)

Arguments

Details

No coordinate transforms are done (unlike in groupLocation, groupShape, groupSpread), i.e., origin is not assumed to be in top-left corner, and points are not taken relative to point of aim.
Uses the rotating calipers algorithm (Toussaint, 1983).

Value

A list with the following information about the minimum-area bounding box:

References

Computational Geometry Algorithms Library. 2021. CGAL Chapter 65: Bounding Volumes. https://doc.cgal.org/Manual/latest/doc_html/cgal_manual/Bounding_volumes/Chapter_main.html Toussaint, G. T. 1983. Solving geometric problems with the rotating calipers. In: Proceedings of the 1983 IEEE MELECON. Athens, Greece: IEEE Computer Society.

See Also

drawBox2, getBoundingBox, getMinCircle

Examples

# coordinates given by a suitable data frame
bb <- getMinBBox(DFsavage)               # minimum bounding box

# plot points and minimum bounding box
plot(point.y ~ point.x, data=DFsavage, asp=1,
     xlim=range(bb$pts[ , 1]), ylim=range(bb$pts[ , 2]), pch=16)
drawBox2(bb, fg='blue', colCtr='blue', pch=4, cex=2)

bb$FoM                                   # figure of merit
bb$angle                                 # box orientation

# coordinates given by a matrix
## Not run: 
xy <- matrix(round(rnorm(16, 100, 15)), ncol=2)
getMinBBox(xy)

## End(Not run)

Description

Calculates center and radius of the minimum enclosing circle given a set of 2D-coordinates.

Usage

getMinCircle(xy)

## S3 method for class 'data.frame'
getMinCircle(xy)

## Default S3 method:
getMinCircle(xy)

Arguments

Details

No coordinate transforms are done (unlike in groupLocation, groupShape, groupSpread), i.e., origin is not assumed to be in top-left corner, and points are not taken relative to point of aim.

Uses the Skyum algorithm based on the convex hull.

Value

A list containing the center and radius of the circle.

References

Computational Geometry Algorithms Library. 2021. CGAL Chapter 65: Bounding Volumes. https://doc.cgal.org/Manual/latest/doc_html/cgal_manual/Bounding_volumes/Chapter_main.html Fischer, K.; Gaertner, B.; Kutz, M. 2003. Fast smallest-enclosing-ball computation in high dimensions. In: Proceedings of the 11th European Symposium on Algorithms (ESA), 630-641. https://github.com/hbf/miniball Gaertner, B. 2021. Miniball: Smallest Enclosing Balls of Points. https://people.inf.ethz.ch/gaertner/subdir/software/miniball.html Skyum, S. 1991. A simple algorithm for computing the smallest enclosing circle. Information Processing Letters 37(3), 121-125. Welzl, E. 1991. Smallest enclosing disks (balls and ellipsoids). In: Maurer H. (eds), New Results and New Trends in Computer Science 555, 359-370. doi 10.1007/BFb0038202.

See Also

drawCircle, getMinBBox, getBoundingBox

Examples

# coordinates given by a suitable data frame
mc <- getMinCircle(DFsavage)

# determine axis limits so that circle will be visible
xLims <- mc$ctr[1] + c(-mc$rad, mc$rad)
yLims <- mc$ctr[2] + c(-mc$rad, mc$rad)
plot(point.y ~ point.x, data=DFsavage,
     pch=16, asp=1, xlim=xLims, ylim=yLims)
drawCircle(mc, fg='blue')

# coordinates given by a matrix
## Not run: 
xy <- matrix(round(rnorm(20, 100, 15), 2), ncol=2)
getMinCircle(xy)

## End(Not run)

Description

Calculates center, shape matrix, and area of the minimum enclosing ellipse given a set of 2D-coordinates using Khachiyan's algorithm.

Usage

getMinEllipse(xy, tol = 0.001, max_iter = 1000)

## S3 method for class 'data.frame'
getMinEllipse(xy, tol = 0.001, max_iter = 1000)

## Default S3 method:
getMinEllipse(xy, tol = 0.001, max_iter = 1000)

Arguments

Details

No coordinate transforms are done (unlike in groupLocation, groupShape, groupSpread), i.e., origin is not assumed to be in top-left corner, and points are not taken relative to point of aim.

Value

A list containing the center, (2 x 2)-shape matrix, and area of the ellipse.

References

Computational Geometry Algorithms Library. 2021. CGAL Chapter 65: Bounding Volumes. https://doc.cgal.org/Manual/latest/doc_html/cgal_manual/Bounding_volumes/Chapter_main.html

Todd MJ and Yildrim EA. On Khachiyan's Algorithm for the Computation of Minimum Volume Enclosing Ellipsoids. Discrete Applied Mathematics 2007: 155: 1731-1744. https://people.orie.cornell.edu/miketodd/TYKhach.pdf

Jacob. Bounding ellipse. https://stackoverflow.com/a/1768440.

See Also

drawEllipse, getMinCircle, getMinBBox, getBoundingBox

Examples

# coordinates given by a suitable data frame
me <- getMinEllipse(DFsavage, tol=0.001)

plot(point.y ~ point.x, data=DFsavage, pch=16, asp=1)
drawEllipse(me, fg='blue')

# coordinates given by a matrix
## Not run: 
xy <- matrix(round(rnorm(20, 100, 15), 2), ncol=2)
getMinEllipse(xy, tol=0.001)

## End(Not run)

Description

Converts object size to angular diameter (degree, radian, minute of angle MOA = arcminute, Shooter's MOA SMOA, milliradian mrad, NATO mil).

Usage

getMOA(x, dst, conversion,
       type = c('deg', 'rad', 'MOA', 'SMOA', 'mrad', 'mil'))

Arguments

Details

1 MOA (minute of angle, arcmin) = 1/60 degree. Shooter's MOA = SMOA = Inches Per Hundred Yards IPHY. 1 inch at 100 yards = 1 SMOA. 1 milliradian = 1/1000 radian. 1 mil = 2*pi/6400 radian (NATO definition: the circle circumference is divided into 6400 mils). Details are given in the vignette, see vignette('shotGroups') .

If package shiny is installed, an interactive web app for this functionality can be run with runGUI("angular").

Value

A numerical vector with the angular diameter values.

See Also

fromMOA, getDistance

Examples

size <- seq(1, 20, by=5)   # inch
dst  <- 100                # yard
getMOA(size, dst=dst, conversion='yd2in', type='MOA')

# this should return objSize
MOA <- getMOA(size, dst=dst, conversion='yd2in', type='MOA')
fromMOA(MOA, dst=dst, conversion='yd2in', type='MOA')

# SMOA
getMOA(c(1, 2, 5), dst=100, conversion='yd2in', type='SMOA')

# milliradian
getMOA(c(10, 20, 50), dst=100, conversion='m2mm', type='mrad')

Description

Returns range statistics: extreme spread, figure of merit, bounding box diagonal

Usage

getRangeStat(xy, dstTarget, conversion)

## S3 method for class 'data.frame'
getRangeStat(xy, dstTarget, conversion)

## Default S3 method:
getRangeStat(xy, dstTarget, conversion)

Arguments

Value

A named numeric vector with elements ES (extreme spread), FoM (figure of merit), D (bounding box diagonal).

References

Grubbs, F. E. (1964b). Statistical measures of accuracy for riflemen and missile engineers. Ann Arbor, ML: Edwards Brothers.

See Also

getMaxPairDist, getBoundingBox

Examples

getRangeStat(DFscar17)

Description

Estimates the radial precision parameter sigma of the Rayleigh distribution together with the radial mean MR and radial standard deviation RSD, including parametric confidence intervals. For 1D data, it estimates the parameters of the half normal distribution. For 3D data, it estimates the parameters of the Maxwell-Boltzmann distribution

Usage

getRayParam(xy, level = 0.95, mu, doRob = FALSE)

## S3 method for class 'data.frame'
getRayParam(xy, level = 0.95, mu, doRob = FALSE)

## Default S3 method:
getRayParam(xy, level = 0.95, mu, doRob = FALSE)

Arguments

Details

When the true mean mu of the distribution is given, the sigma estimate uses the sum of squared radii for the variance estimate (the total un-corrected variance of the coordinates), and employs the c4 correction factor for taking the square root. When mu is missing, the sum of squared radii is Bessel-corrected for estimating the center.

The robust estimate for the covariance matrix of (x,y)-coordinates is from covMcd using the MCD algorithm.

Value

A list with the estimates for sigma, RSD, and MR including the confidence intervals.

References

http://ballistipedia.com/index.php?title=Closed_Form_Precision

Singh, H. P. 1992. Estimation of Circular Probable Error. The Indian Journal of Statistics, Series B 5(3), 289-305.

See Also

Rayleigh, Maxwell, getCEP, getHitProb, groupSpread, covMcd

Examples

# coordinates given by a suitable data frame
getRayParam(DFtalon, level=0.95, doRob=FALSE)

# coordinates given by a matrix
## Not run: 
xy <- matrix(round(rnorm(100, 0, 5), 2), ncol=2)
getRayParam(xy, level=0.95, doRob=FALSE)

## End(Not run)

Description

Estimates the location parameter nu and the scale parameter sigma of the Rice distribution together with the radial mean MR and radial standard deviation RSD based on a set of 2D-coordinates. Includes the parametric confidence interval for sigma.

Usage

getRiceParam(xy, level = 0.95, doRob = FALSE, type = c('LiZhangDai', 'MOM'))

## S3 method for class 'data.frame'
getRiceParam(xy, level = 0.95, doRob = FALSE, type=c('LiZhangDai', 'MOM'))

## Default S3 method:
getRiceParam(xy, level = 0.95, doRob = FALSE, type=c("LiZhangDai", 'MOM'))

Arguments

Details

The sigma estimate uses getRayParam. The robust estimate for the center and for the covariance matrix of (x,y,z)-coordinates is from covMcd using the MCD algorithm.

Value

A list with the estimates for nu, sigma, RSD, and MR including the confidence interval for sigma.

References

https://reference.wolfram.com/language/ref/RiceDistribution.html

Li, Q., Zhang, J., & Dai, S. (2009). On estimating the non-centrality parameter of a chi-squared distribution. Statistics and Probability Letters 79, 98-114.

See Also

Rice, getRayParam, getCEP, getHitProb, covMcd

Examples

getRiceParam(DF300BLKhl, level=0.95, doRob=FALSE)

# coordinates given by a matrix
## Not run: 
xy <- matrix(round(rnorm(60, 0, 5), 2), ncol=2)
getRiceParam(xy, level=0.95, doRob=FALSE)

## End(Not run)

Description

Extracts (x,y)- or (x,y,z)-coordinates of the points of impact (relative to the point of aim) from a data frame and returns them as a matrix.

Usage

getXYmat(DF, xyTopLeft = TRUE, relPOA = TRUE, center = FALSE)

Arguments

Details

By default, OnTarget PC/TDS' 'Export Point Data' places the origin of the absolute coordinate system in the top-left corner. In OnTarget TDS, this setting can be changed by checking the box 'Tools -> Options -> Options tab -> Data Export -> Invert Y-Axis on Export'. In that case, use xyTopLeft=FALSE. If groups appear to be upside-down, xyTopLeft is the setting to change.

Value

A numerical matrix with the (x,y)- or (x,y,z)-coordinates.

See Also

groupLocation, groupShape, groupSpread

Examples

data(DFcm)

# select data from only first series
DFsub <- subset(DFcm, series == 1)
getXYmat(DFsub, xyTopLeft=TRUE, relPOA=TRUE)

Description

Calculates location measures for a single group of bullet holes.

Usage

groupLocation(xy, level = 0.95, plots = TRUE, bootCI = 'none',
              dstTarget, conversion)

## S3 method for class 'data.frame'
groupLocation(xy, level = 0.95, plots = TRUE, bootCI = 'none',
              dstTarget, conversion)

## Default S3 method:
groupLocation(xy, level = 0.95, plots = TRUE, bootCI = 'none',
              dstTarget, conversion)

Arguments

Details

The number of replicates for the reported bootstrap confidence intervals is at least 1499. If the BCa interval is reported, it is at least the number of points.

If package shiny is installed, an interactive web app for this functionality can be run with runGUI("analyze").

Value

A list with the results from the numerical analyses and statistical tests.

See Also

getMOA, covMcd, anova.mlm, boot, boot.ci

Examples

# coordinates given by a suitable data frame
res <- groupLocation(DFsavage, dstTarget=100, conversion='m2mm',
                     level=0.95, plots=2, bootCI='basic')
names(res)
res$ctr
res$distPOA
res$ctrXci
res$ctrYci

# coordinates given by a matrix
## Not run: 
# assume data from pistol shooting at 25m with 9mm ammo
# metric units
xy <- matrix(round(rnorm(100, 0, 5), 2), ncol=2)
groupLocation(xy, dstTarget=25, conversion='m2cm', plots=2)

## End(Not run)

Description

Assesses shape of a single group of bullet holes: Outlier analysis as well as numerical and graphical normality checks for a set of (x,y)-coordinates.

Usage

groupShape(xy, center = FALSE, plots = TRUE, bandW = 0.5,
           outlier = c('mcd', 'pca'), dstTarget, conversion, ...)

## S3 method for class 'data.frame'
groupShape(xy, center = FALSE, plots = TRUE, bandW = 0.5,
           outlier=c('mcd', 'pca'), dstTarget, conversion, ...)

## Default S3 method:
groupShape(xy, center = FALSE, plots = TRUE, bandW = 0.5,
           outlier=c('mcd', 'pca'), dstTarget, conversion, ...)