Package 'alphaOutlier' reference manual

Title:	Obtain Alpha-Outlier Regions for Well-Known Probability Distributions
Description:	Given the parameters of a distribution, the package uses the concept of alpha-outliers by Davies and Gather (1993) to flag outliers in a data set. See Davies, L.; Gather, U. (1993): The identification of multiple outliers, JASA, 88 423, 782-792, <doi:10.1080/01621459.1993.10476339> for details.
Authors:	Andre Rehage, Sonja Kuhnt
Maintainer:	Andre Rehage <[email protected]>
License:	GPL-3
Version:	1.2.0
Built:	2024-12-15 07:31:07 UTC
Source:	CRAN

Obtain $\alpha$ -outlier regions for well-known probability distributions

Description

Given the parameters of a distribution, the package uses the concept of $\alpha$ -outliers by Davies and Gather (1993) to flag outliers in a data set.

Details

The structure of the package is as follows: aout.[Distribution] is the name of the function which returns the $\alpha$ -outlier region of a random variable following [Distribution]. The names of the distributions are abbreviated as in the d, p, q, r functions. Use pre-specified or robustly estimated parameters from your data to obtain reasonable results. The sample size should be taken into account when choosing alpha, for example Gather et al. (2003) propose $\alpha_N = 1 - (1 - \alpha)^{1/N}$ .

Author(s)

A. Rehage, S. Kuhnt

References

Davies, L.; Gather, U. (1993) The identification of multiple outliers, Journal of the American Statistical Association, 88 423, 782-792.

Gather, U.; Kuhnt, S.; Pawlitschko, J. (2003) Concepts of outlyingness for various data structures. In J. C. Misra (Ed.): Industrial Mathematics and Statistics. New Delhi: Narosa Publishing House, 545-585.

Examples


iris.setosa <- iris[1:51, 4]
aout.norm(data = iris.setosa, param = c(mean(iris.setosa), sd(iris.setosa)), alpha = 0.01)
aout.pois(data = warpbreaks[,1], param = mean(warpbreaks[,1]), alpha = 0.01, 
          hide.outliers = TRUE)
iris.setosa <- iris[1:51, 4]
aout.norm(data = iris.setosa, param = c(mean(iris.setosa), sd(iris.setosa)), alpha = 0.01)
aout.pois(data = warpbreaks[,1], param = mean(warpbreaks[,1]), alpha = 0.01, 
          hide.outliers = TRUE)

Find $\alpha$ -outliers in Binomial data

Description

Given the parameters of a Binomial distribution, aout.binom identifies $\alpha$ -outliers in a given data set.

Usage

aout.binom(data, param, alpha = 0.1, hide.outliers = FALSE)
aout.binom(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

`data`	a vector. The data set to be examined.
`param`	a vector. Contains the parameters of the Binomial distribution, $N$ and $p$ .
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

Examples

data(uis)
medbeck <- median(uis$BECK) 
aout.binom(data = uis$BECK, param = c(54, medbeck/54), alpha = 0.001)
data(uis)
medbeck <- median(uis$BECK) 
aout.binom(data = uis$BECK, param = c(54, medbeck/54), alpha = 0.001)

Find $\alpha$ -outliers in conditional Gaussian data

Description

Given the parameters of a conditional Gaussian distribution, aout.cg identifies $\alpha$ -outliers in a given data set.

Usage

aout.cg(data, param, alpha = 0.1, hide.outliers = FALSE)
aout.cg(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

`data`	a matrix. First column: Class of the value, coded with an integer between 1 and d, where d is the number of classes. Second column: The value as a realization of a univariate normal with parameters $\mu$ and $\sigma$ . The data set to be examined.
`param`	a list with three elements: `p`: d-dimensional vector of probabilities of the classes. `mu`: d-dimensional vector of univariate mean values of each class. `sigma`: d-dimensional vector of univariate standard errors of each class
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a data frame of the outlier-free data.

Author(s)

A. Rehage

References

Edwards, D. (2000) Introduction to Graphical Modelling. 2nd edition, Springer, New York.

Kuhnt, S.; Rehage, A. (2013) The concept of $\alpha$ -outliers in structured data situations. In C. Becker, R. Fried, S. Kuhnt (Eds.): Robustness and Complex Data Structures. Festschrift in Honour of Ursula Gather. Berlin: Springer, 91-108.

Examples

# Rats' weights data example taken from Edwards (2000)
ratweight <- cbind(Drug = c(1, 1, 2, 3, 1, 1, 2, 3, 1, 2, 3, 3, 1, 2, 2, 3, 1, 
                            2, 2, 3, 1, 2, 3, 3), 
                   Week1 = c(5, 7, 9, 14, 7, 8, 7, 14, 9, 7, 21, 12, 5, 7, 6, 
                             17, 6, 10, 6, 14, 9, 8, 16, 10))
aout.cg(ratweight, 
        list(p = c(1/3, 1/3, 1/3), mu = c(7, 7, 14), sigma = c(1.6, 1.4, 3.3)))
# Rats' weights data example taken from Edwards (2000)
ratweight <- cbind(Drug = c(1, 1, 2, 3, 1, 1, 2, 3, 1, 2, 3, 3, 1, 2, 2, 3, 1, 
                            2, 2, 3, 1, 2, 3, 3), 
                   Week1 = c(5, 7, 9, 14, 7, 8, 7, 14, 9, 7, 21, 12, 5, 7, 6, 
                             17, 6, 10, 6, 14, 9, 8, 16, 10))
aout.cg(ratweight, 
        list(p = c(1/3, 1/3, 1/3), mu = c(7, 7, 14), sigma = c(1.6, 1.4, 3.3)))

Find $\alpha$ -outliers in $\chi^2$ data

Description

Given the parameters of a $\chi^2$ distribution, aout.chisq identifies $\alpha$ -outliers in a given data set.

Usage

aout.chisq(data, param, alpha = 0.1, hide.outliers = FALSE, ncp = 0, lower = auto.l,
           upper = auto.u, method.in = "Newton", global.in = "gline", 
           control.in = list(sigma = 0.1, maxit = 1000, xtol = 1e-12, 
                             ftol = 1e-12, btol = 1e-04))
aout.chisq(data, param, alpha = 0.1, hide.outliers = FALSE, ncp = 0, lower = auto.l,
           upper = auto.u, method.in = "Newton", global.in = "gline", 
           control.in = list(sigma = 0.1, maxit = 1000, xtol = 1e-12, 
                             ftol = 1e-12, btol = 1e-04))

Arguments

`data`	a vector. The data set to be examined.
`param`	an atomic vector. Contains the degrees of freedom of the $\chi^2$ distribution.
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to $0.1$ .
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.
`ncp`	an atomic vector. Determines the non-centrality parameter of the $\chi^2$ distribution. Defaults to 0.
`lower`	an atomic vector. First element of `x` from `nleqslv`.
`upper`	an atomic vector. Second element of `x` from `nleqslv`.
`method.in`	See `method` in `nleqslv`.
`global.in`	See `global` in `nleqslv`.
`control.in`	See `control` in `nleqslv`.

Details

The $\alpha$ -outlier region of a $\chi^2$ distribution is generally not available in closed form or via the tails, such that a non-linear equation system has to be solved.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

Examples

aout.chisq(chisq.test(occupationalStatus)$statistic, 49)
aout.chisq(chisq.test(occupationalStatus)$statistic, 49)

Find $\alpha$ -outliers in two-way contingency tables

Description

This is a wrapper function for aout.pois. We assume that each entry of a contingency table can be seen as a realization of a Poisson random variable. The parameter $\lambda$ of each cell can either be set by the user or estimated. Given the parameters, aout.conttab identifies $\alpha$ -outliers in a given contingency table.

Usage

aout.conttab(data, param, alpha = 0.1, hide.outliers = FALSE, show.estimates = FALSE)
aout.conttab(data, param, alpha = 0.1, hide.outliers = FALSE, show.estimates = FALSE)

Arguments

`data`	a matrix or data.frame. The contingency table to be examined.
`param`	a character string from `c("ML", "L1", "MP")` or a vector containing the parameters of each cell of the Poisson distribution: $\lambda$ . `"ML"` yields the maximum likelihood estimate from the log-linear Poisson model using a suitable design matrix. `"L1"` yields the L1-estimate from `rq.fit.fnc`. `"MP"` yields the Median Polish estimate. If the parameter vector is given by the user, it is necessary that the contingency table was filled `byrow = FALSE`.
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.
`show.estimates`	boolean. Returns $\hat{\lambda}$ for each cell if set to `TRUE`. Defaults to `FALSE`.

Value

Data frame of the vectorized input data and, if desired, an index named is.outlier that flags the outliers with TRUE and a vector named param containing the estimated lambdas.

Author(s)

A. Rehage

References

Kuhnt, S. (2000) Ausreisseridentifikation im Loglinearen Poissonmodell fuer Kontingenztafeln unter Einbeziehung robuster Schaetzer. Ph.D. Thesis. Universitaet Dortmund, Dortmund. Fachbereich Statistik.

Kuhnt, S.; Rapallo, F.; Rehage, A. (2014) Outlier detection in contingency tables based on minimal patterns. Statistics and Computing 24 (3), 481-491.

Examples

aout.conttab(data = HairEyeColor[,,1], param = "L1", alpha = 0.01, show.estimates = TRUE)
aout.conttab(data = HairEyeColor[,,1], param = "ML", alpha = 0.01, show.estimates = TRUE)
aout.conttab(data = HairEyeColor[,,1], param = "L1", alpha = 0.01, show.estimates = TRUE)
aout.conttab(data = HairEyeColor[,,1], param = "ML", alpha = 0.01, show.estimates = TRUE)

Find $\alpha$ -outliers in exponentially distributed data

Description

Given the parameters of an exponential distribution, aout.exp identifies $\alpha$ -outliers in a given data set.

Usage

aout.exp(data, param, alpha = 0.1, hide.outliers = FALSE, theta = 0)
aout.exp(data, param, alpha = 0.1, hide.outliers = FALSE, theta = 0)

Arguments

`data`	a vector. The data set to be examined.
`param`	an atomic vector. Contains the parameter of the exponential distribution.
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.
`theta`	an atomic vector. Determines the lower bound of the support of the exponential distribution. Defaults to 0.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

References

Examples

aout.exp(attenu[,5], median(attenu[,5]), alpha = 0.05)
aout.exp(attenu[,5], median(attenu[,5]), alpha = 0.05)

Find $\alpha$ -outliers in data from the family of $g$ -and- $h$ distributions

Description

Given the parameters of a $g$ -and- $h$ distribution, aout.gandh identifies $\alpha$ -outliers in a given data set.

Usage

aout.gandh(data, param, alpha = 0.1, hide.outliers = FALSE)
aout.gandh(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

`data`	a vector. The data set to be examined.
`param`	a vector. Contains the parameters of the $g$ -and- $h$ distribution: median, scale, $g$ , $h$ .
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.

Details

The concept of $\alpha$ -outliers is based on the p.d.f. of the random variable. Since for $g$ -and- $h$ distributions this does not exist in closed form, the computation of the outlier region is based on an optimization of the quantile function with side conditions.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Note

Makes use of solnp.

Author(s)

A. Rehage

References

Xu, Y.; Iglewicz, B.; Chervoneva, I. (2014) Robust estimation of the parameters of g-and-h distributions, with applications to outlier detection. Computational Statistics and Data Analysis 75, 66-80.

Examples

durations <- faithful$eruptions
aout.gandh(durations, c(4.25, 1.14, 0.05, 0.05), alpha = 0.1)
durations <- faithful$eruptions
aout.gandh(durations, c(4.25, 1.14, 0.05, 0.05), alpha = 0.1)

Find $\alpha$ -outliers in hypergeometric data

Description

Given the parameters of a hypergeometric distribution, aout.hyper identifies $\alpha$ -outliers in a given data set.

Usage

aout.hyper(data, param, alpha = 0.1, hide.outliers = FALSE)
aout.hyper(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

`data`	a vector. The data set to be examined.
`param`	a vector. Contains the parameters of the hypergeometric distribution: $m, n, k$ .
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

Examples

set.seed(1)
lotto6aus49 <- rhyper(100, 6, 43, 6) 
aout.hyper(lotto6aus49, c(6, 43, 6), 0.1)
set.seed(1)
lotto6aus49 <- rhyper(100, 6, 43, 6) 
aout.hyper(lotto6aus49, c(6, 43, 6), 0.1)

Find $\alpha$ -outliers in arbitrary univariate data using kernel density estimation

Description

Given the arguments of the density, aout.kernel identifies $\alpha$ -outliers in a given data set.

Usage

aout.kernel(data, alpha, plot = TRUE, plottitle = "", kernel = "gaussian", 
nkernel = 1024, kern.bw = "SJ", kern.adj = 1, 
xlim = NA, ylim = NA, outints = FALSE, w = NA, ...)
aout.kernel(data, alpha, plot = TRUE, plottitle = "", kernel = "gaussian", 
nkernel = 1024, kern.bw = "SJ", kern.adj = 1, 
xlim = NA, ylim = NA, outints = FALSE, w = NA, ...)

Arguments

`data`	a vector. The data set to be examined.
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain.
`plot`	boolean. If `TRUE`, a plot of the data and estimated density with shaded outlier region is printed.
`plottitle`	character string. Title of the plot.
`kernel`	See `kernel` in `density`.
`nkernel`	See `n` in `density`.
`kern.bw`	See `bw` in `density`.
`kern.adj`	See `adjust` in `density`.
`xlim`	a vector. Specify if you want to change the x-limits of the plot.
`ylim`	a vector. Specify if you want to change the y-limits of the plot.
`outints`	boolean. If `TRUE`, then the bounds of the inlier-regions and the chosen bandwidth are shown.
`w`	a vector. See `weights` in `density`.
`...`	Further arguments for `density` and `plot`.

Value

If outints = TRUE, a list of

`Results`	A data frame containing one row for each observation. The observations are labelled whether they are outlying, the value of the estimated density at the observation is shown and the bound of the outlier identifier.
`Bounds.of.Inlier.Regions`	The bounds of the inlier region(s).
`KDE.Chosen.Bandwidth`	The bandwidth that was chosen by `density`.

Author(s)

A. Rehage

Examples

set.seed(23)
tempx <- rnorm(1000, 0, 1)
tempx[1] <- -2.5
aout.kernel(tempx[1:10], alpha = 0.1, kern.adj = 1, xlim = c(-3,3), outints = TRUE)
# not run:
# aout.kernel(tempx[1:200], alpha = 0.1, kern.adj = 1, xlim = c(-3,3))
set.seed(23)
tempx <- rnorm(1000, 0, 1)
tempx[1] <- -2.5
aout.kernel(tempx[1:10], alpha = 0.1, kern.adj = 1, xlim = c(-3,3), outints = TRUE)
# not run:
# aout.kernel(tempx[1:200], alpha = 0.1, kern.adj = 1, xlim = c(-3,3))

Find $\alpha$ -outliers in Laplace / double exponential data

Description

Given the parameters of a Laplace distribution, aout.laplace identifies $\alpha$ -outliers in a given data set.

Usage

aout.laplace(data, param, alpha = 0.1, hide.outliers = FALSE)
aout.laplace(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

`data`	a vector. The data set to be examined.
`param`	a vector. Contains the parameters of the Laplace distribution: $\mu, \sigma$ .
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

References

Dumonceaux, R.; Antle, C. E. (1973) Discrimination between the log-normal and the Weibull distributions. Technometrics, 15 (4), 923-926.

Examples

# Using the flood data from Dumonceaux and Antle (1973):
temp <- c(0.265, 0.269, 0.297, 0.315, 0.3225, 0.338, 0.379, 0.380, 0.392, 0.402,
         0.412, 0.416, 0.418, 0.423, 0.449, 0.484, 0.494, 0.613, 0.654, 0.74)
aout.laplace(temp, c(median(temp), median(abs(temp - median(temp)))), 0.05)
# Using the flood data from Dumonceaux and Antle (1973):
temp <- c(0.265, 0.269, 0.297, 0.315, 0.3225, 0.338, 0.379, 0.380, 0.392, 0.402,
         0.412, 0.416, 0.418, 0.423, 0.449, 0.484, 0.494, 0.613, 0.654, 0.74)
aout.laplace(temp, c(median(temp), median(abs(temp - median(temp)))), 0.05)

Find $\alpha$ -outliers in logistic data

Description

Given the parameters of a logistic distribution, aout.logis identifies $\alpha$ -outliers in a given data set.

Usage

aout.logis(data, param, alpha = 0.1, hide.outliers = FALSE)
aout.logis(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

`data`	a vector. The data set to be examined.
`param`	a vector. Contains the parameters of the logistic distribution: $\mu, \sigma$ .
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

References

Balakrishnan, N. (1992) Maximum likelihood estimation based on complete and type II censored samples. In N. Balakrishnan (Ed.): Handbook of the Logistic Distribution. Dekker, New York, 49-78.

Examples

# Data example from Balakrishnan (1967)
lifetime <- c(785, 855, 905, 918, 919, 920, 929, 936, 948, 950)
aout.logis(lifetime, c(949.9, 63.44))
# Data example from Balakrishnan (1967)
lifetime <- c(785, 855, 905, 918, 919, 920, 929, 936, 948, 950)
aout.logis(lifetime, c(949.9, 63.44))

Find $\alpha$ -outliers in multivariate normal data

Description

Given the parameters of a multivariate normal distribution, aout.mvnorm identifies $\alpha$ -outliers in a given data set.

Usage

aout.mvnorm(data, param, alpha = 0.1, hide.outliers = FALSE)
aout.mvnorm(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

`data`	a data.frame or matrix. The data set to be examined.
`param`	a list. Contains the parameters of the normal distribution: the mean vector $\mu$ and the covariance matrix $\sigma$ .
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a data frame of the outlier-free data.

Author(s)

A. Rehage

References

Examples

temp <- iris[1:51,-5]
temp.xq <- apply(FUN = median, MARGIN = 2, temp)
aout.mvnorm(as.matrix(temp), param = list(temp.xq, cov(temp)), alpha = 0.001)
temp <- iris[1:51,-5]
temp.xq <- apply(FUN = median, MARGIN = 2, temp)
aout.mvnorm(as.matrix(temp), param = list(temp.xq, cov(temp)), alpha = 0.001)

Find $\alpha$ -outliers in negative Binomial data

Description

Given the parameters of a negative Binomial distribution, aout.nbinom identifies $\alpha$ -outliers in a given data set.

Usage

aout.nbinom(data, param, alpha = 0.1, hide.outliers = FALSE)
aout.nbinom(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

`data`	a vector. The data set to be examined.
`param`	a vector. Contains the parameters of the negative Binomial distribution: $N, p$ .
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

Examples

data(daysabs)
aout.nbinom(daysabs, c(8, 0.6), 0.05)
data(daysabs)
aout.nbinom(daysabs, c(8, 0.6), 0.05)

Find $\alpha$ -outliers in normal data

Description

Given the parameters of a normal distribution, aout.norm identifies $\alpha$ -outliers in a given data set.

Usage

aout.norm(data, param = c(0, 1), alpha = 0.1, hide.outliers = FALSE)
aout.norm(data, param = c(0, 1), alpha = 0.1, hide.outliers = FALSE)

Arguments

`data`	a vector. The data set to be examined.
`param`	a vector. Contains the parameters of the normal distribution: $\mu, \sigma$ .
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

References

Examples

iris.setosa <- iris[1:51, 4]
# implosion breakdown point:
aout.norm(data = iris.setosa, param = c(median(iris.setosa), mad(iris.setosa)), 
          alpha = 0.01) 
# better:
aout.norm(data = iris.setosa, param = c(median(iris.setosa), sd(iris.setosa)), 
          alpha = 0.01) 
iris.setosa <- iris[1:51, 4]
# implosion breakdown point:
aout.norm(data = iris.setosa, param = c(median(iris.setosa), mad(iris.setosa)), 
          alpha = 0.01) 
# better:
aout.norm(data = iris.setosa, param = c(median(iris.setosa), sd(iris.setosa)), 
          alpha = 0.01)

Find $\alpha$ -outliers in Pareto data

Description

Given the parameters of a Pareto distribution, aout.pareto identifies $\alpha$ -outliers in a given data set.

Usage

aout.pareto(data, param, alpha = 0.1, hide.outliers = FALSE)
aout.pareto(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

`data`	a vector. The data set to be examined.
`param`	a vector. Contains the parameters of the Pareto distribution: $\lambda, \theta$ .
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.

Details

We use the Pareto distribution with Lebesgue-density $f(x) = \frac{\lambda \theta^{\lambda}}{x^{\lambda + 1}}$ .

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

References

Examples

data(citiesData)
aout.pareto(citiesData[[1]], c(1.31, 14815), alpha = 0.01)
data(citiesData)
aout.pareto(citiesData[[1]], c(1.31, 14815), alpha = 0.01)

Find $\alpha$ -outliers in Poisson count data

Description

Given the parameters of a Poisson distribution, aout.pois identifies $\alpha$ -outliers in a given data set.

Usage

aout.pois(data, param, alpha = 0.1, hide.outliers = FALSE)
aout.pois(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

`data`	a vector. The data set to be examined.
`param`	a vector. Contains the parameter of the Poisson distribution: $\lambda$ .
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

Examples

aout.pois(data = c(discoveries), param = median(discoveries), alpha = 0.01)
aout.pois(data = c(discoveries), param = median(discoveries), alpha = 0.01)

Find $\alpha$ -outliers in Weibull data

Description

Given the parameters of a Weibull distribution, aout.weibull identifies $\alpha$ -outliers in a given data set.

Usage

aout.weibull(data, param, alpha = 0.1, hide.outliers = FALSE, lower = auto.l, 
             upper = auto.u, method.in = "Broyden", global.in = "qline", 
             control.in = list(sigma = 0.1, maxit = 1000, xtol = 1e-12, 
                               ftol = 1e-12, btol = 1e-04))
aout.weibull(data, param, alpha = 0.1, hide.outliers = FALSE, lower = auto.l, 
             upper = auto.u, method.in = "Broyden", global.in = "qline", 
             control.in = list(sigma = 0.1, maxit = 1000, xtol = 1e-12, 
                               ftol = 1e-12, btol = 1e-04))

Arguments

`data`	a vector. The data set to be examined.
`param`	a vector. Contains the parameters of the Weibull distribution: $\beta, \lambda$ .
`alpha`	an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.
`hide.outliers`	boolean. Returns the outlier-free data if set to `TRUE`. Defaults to `FALSE`.
`lower`	an atomic vector. First element of `x` from `nleqslv`.
`upper`	an atomic vector. Second element of `x` from `nleqslv`.
`method.in`	See `method` in `nleqslv`
`global.in`	See `global` in `nleqslv`
`control.in`	See `control` in `nleqslv`

Details

The $\alpha$ -outlier region of a Weibull distribution is generally not available in closed form or via the tails, such that a non-linear equation system has to be solved.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

References

Dodson, B. (2006) The Weibull Analysis Handbook. American Society for Quality, 2nd edition.

Examples

# lifetime data example taken from Table 2.2, Dodson (2006)
temp <- c(12.5, 24.4, 58.2, 68.0, 69.1, 95.5, 96.6, 97.0, 
          114.2, 123.2, 125.6, 152.7)
aout.weibull(temp, c(2.25, 97), 0.1)
# lifetime data example taken from Table 2.2, Dodson (2006)
temp <- c(12.5, 24.4, 58.2, 68.0, 69.1, 95.5, 96.6, 97.0, 
          114.2, 123.2, 125.6, 152.7)
aout.weibull(temp, c(2.25, 97), 0.1)

Population of the 999 largest German cities

Description

Population of the 999 largest German cities as a real life example for Pareto distributed data

Usage

data(citiesData)data(citiesData)

Format

List with one element

References

http://bevoelkerungsstatistik.de

Create design matrix for log-linear models of contingency tables

Description

This function creates a design matrix for contingency tables and is particularly useful for log-linear Poisson models. It uses effect coding of the variables: First the rows of the contingency table from top to bottom, then the columns from left to right.

Usage

createDesMat(n, p)
createDesMat(n, p)

Arguments

`n`	Number of rows of the corresponding contingency table.
`p`	Number of columns of the corresponding contingency table.

Value

A (n+p-1) times (n*p) design matrix.

Author(s)

A. Rehage

References

Kuhnt, S.; Rapallo, F.; Rehage, A. (2014) Outlier detection in contingency tables based on minimal patterns. Statistics and Computing 24 (3), 481-491.

Examples

createDesMat(3, 5)
createDesMat(3, 5)

Number of absence days of students

Description

Number of absence days of students

Usage

data(daysabs)data(daysabs)

Format

Vector with 314 elements

References

http://www.ats.ucla.edu/stat/r/dae/nbreg.htm

Package 'alphaOutlier'

Help Index

Obtain α\alphaα-outlier regions for well-known probability distributions

Description

Details

Author(s)

References

See Also

Examples

Find α\alphaα-outliers in Binomial data

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Find α\alphaα-outliers in conditional Gaussian data

Description

Usage

Arguments

Value

Author(s)

References

Examples

Find α\alphaα-outliers in χ2\chi^2χ2 data

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Find α\alphaα-outliers in two-way contingency tables

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Find α\alphaα-outliers in exponentially distributed data

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Find α\alphaα-outliers in data from the family of ggg-and-hhh distributions

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

Examples

Find α\alphaα-outliers in hypergeometric data

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Find α\alphaα-outliers in arbitrary univariate data using kernel density estimation

Description

Usage

Arguments

Value

Author(s)

Examples

Find α\alphaα-outliers in Laplace / double exponential data

Description

Usage

Obtain $\alpha$ -outlier regions for well-known probability distributions

Find $\alpha$ -outliers in Binomial data

Find $\alpha$ -outliers in conditional Gaussian data

Find $\alpha$ -outliers in $\chi^2$ data

Find $\alpha$ -outliers in two-way contingency tables

Find $\alpha$ -outliers in exponentially distributed data

Find $\alpha$ -outliers in data from the family of $g$ -and- $h$ distributions

Find $\alpha$ -outliers in hypergeometric data

Find $\alpha$ -outliers in arbitrary univariate data using kernel density estimation

Find $\alpha$ -outliers in Laplace / double exponential data

Find $\alpha$ -outliers in logistic data

Find $\alpha$ -outliers in multivariate normal data

Find $\alpha$ -outliers in negative Binomial data

Find $\alpha$ -outliers in normal data

Find $\alpha$ -outliers in Pareto data

Find $\alpha$ -outliers in Poisson count data

Find $\alpha$ -outliers in Weibull data