| Title: | Neutrosophic Statistics |
|---|---|
| Description: | Analyzes data involving imprecise and vague information. Provides summary statistics and describes the characteristics of neutrosophic data, as defined by Florentin Smarandache (2013).<ISBN:9781599732749>. |
| Authors: | Zahid Khan [aut], Zsolt T. Kosztyan [aut, cre] |
| Maintainer: | Zsolt T. Kosztyan <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.0.2 |
| Built: | 2024-11-25 16:16:49 UTC |
| Source: | CRAN |
This dataset provides low and high recordings of daily temperature for five different citites (Gujranwala,Lahore,Islambad, Karachi and Sialkot ) of Pakistan for the specifed priod July 2022
data("citytemp")data("citytemp")
A data frame with 28 observations on the following 12 variables.
Daya character vector
Datea numeric vector
Gujranwala_Lowa numeric vector
Gujranwala_Higha numeric vector
Lahore_Lowa numeric vector
Lahore_Higha numeric vector
Karachi_Lowa numeric vector
Karachi_Higha numeric vector
Islamabad_Lowa numeric vector
Islamabad_Higha numeric vector
Sialkot_Lowa numeric vector
Sialkot_Higha numeric vector
The data was collected for each city over 31 days in July 2022. It includes both the lower and upper temperature values, and can be analyzed using neutrosophic statistical approach.
https://www.gismeteo.com/
Ishmal Shahzadi (2023): Neutrosophic Statistical Analysis of Temperature of Different Cities of Pakistan. Neutrosophic Sets and Systems, 53(1). doi:10.5281/zenodo.7535991
# list of temperature data for Gujranwala city G <- mapply(function(low, high) list(c(low, high)), citytemp$Gujranwala_Low, citytemp$Gujranwala_High) # Neutrosophic mean and standard deviation of temperature data for Gujranwala city nmean(G) nstd(G)# list of temperature data for Gujranwala city G <- mapply(function(low, high) list(c(low, high)), citytemp$Gujranwala_Low, citytemp$Gujranwala_High) # Neutrosophic mean and standard deviation of temperature data for Gujranwala city nmean(G) nstd(G)
This dataset contains the estimated average daily ingestion of dioxins from food samples collected across Japan, including uncertainties in the values. Dioxins are toxic chemical compounds that pose significant health risks.
data("dioxin")data("dioxin")
The format is: List of 17 numeric interval values
This data provides an analysis of dioxin intake and its potential health impacts including exposure levels from various food sources in Japan.
The dataset was collected and monitored by the Ministry of Environment, Japan, as reported in their environmental statistics
Zahid Khan, Mohammed M. A. Almazah, Omalsad Hamood Odhah, and Huda M. Alshanbari (2022): Generalized Pareto Model: Properties and Applications in Neutrosophic Data Modeling. Mathematical Problems in Engineering, 2022(1). doi:10.1155/2022/3686968
data(dioxin) # Provide neutrosophic summary statistics nsummary(dioxin)data(dioxin) # Provide neutrosophic summary statistics nsummary(dioxin)
The dataset provides the monthly high and low prices (in rupees per gram) of 22-carat gold in six Indian cities: Chennai, Kolkatta,Bangal, .Data were collected from February 2022 to January 2023. This data can be used for neutrosophic statistical analysis of gold price trends.
data("goldprice")data("goldprice")
A data frame with 12 observations on the following 13 variables.
Montha character vector
Chennai_Lowa numeric vector
Chennai_Higha numeric vector
Kolkatta_Lowa numeric vector
Kolkatta_Higha numeric vector
Bangalore_Lowa numeric vector
Bangalore_Higha numeric vector
Madurai_Lowa numeric vector
Madurai_Higha numeric vector
Hyderabad_Lowa numeric vector
Hyderabad_Higha numeric vector
Delhi_Lowa numeric vector
Delhi_Higha numeric vector
Monthly high and low gold prices in Chennai, Kolkatta, and Bangalore. These can be analyzed using neutrosophic statistical methods to evaluate variations and trends.
Indian Daily Gold Prices Android App
Kala Raja Mohan, R. Narmada Devi, Nagadevi Bala Nagaram, T. Bharathi, and Suresh Rasappan (2023): Neutrosophic Statistical Analysis on Gold Rate. Neutrosophic Sets and Systems, 60(1). doi:10.5281/zenodo.7535991
#list of low and high gold price for Chennai City ch<- mapply(function(low, high) list(c(low, high)), goldprice$Chennai_Low, goldprice$Chennai_High) # neutrosophic coefficient of variation ncv(ch)#list of low and high gold price for Chennai City ch<- mapply(function(low, high) list(c(low, high)), goldprice$Chennai_Low, goldprice$Chennai_High) # neutrosophic coefficient of variation ncv(ch)
This function is used to find sum of more than one imprecise data values.
interval_add(data)interval_add(data)
data |
List of neutrosophic numbers.This numeric list contains at least two neutrosophic intervals. Each interval value should contains two elements, lower and upper.If it crisp value is used,it is considered as an interval with same upper and lower value. |
A numeric vector of length 2,indicating a summed value of neutrosophic intervals
Zahid Khan
Moore, R. E. (1979): Methods and applications of interval analysis.SIAM. doi:10.1137/1.9781611970906
Smarandache, F (2022):Neutrosophic Statistics is an extension of Interval Statistics, while Plithogenic Statistics is the most general form of statistics(second version).Internation journal of neutrosophic science. 19(1),pp.148-165. doi:10.54216/IJNS.190111
#Addition of to neutrosopic numbers x=list(c(5,10),c(10,20)) interval_add(x)#Addition of to neutrosopic numbers x=list(c(5,10),c(10,20)) interval_add(x)
Interval conversion for neutrosophic numbers
interval_df(data)interval_df(data)
data |
data is a vector or a list of neutrosophic numbers |
Data frame of neutrosophic numbers.
Zahid Khan
Florentin Smarandache (2014): Introduction to Neutrosophic Statistics. ISBN: 9781599732749
# values are interval forms as required in neutrosophic data data <- list(c(6, 6), c(2, 8), c(30,50), c(18, 24)) interval_df(data)# values are interval forms as required in neutrosophic data data <- list(c(6, 6), c(2, 8), c(30,50), c(18, 24)) interval_df(data)
This function is used to find an interval division of the neutrosophic numbers
interval_div(data)interval_div(data)
data |
List of neutrosophic numbers.This numeric list contains at least two neutrosophic intervals. Each interval value should contains two elements, lower and upper.If it crisp value is used,it is considered as an interval with same upper and lower value. |
A numeric vector of length 2,indicating a divided value of neutrosophic intervals
Zahid Khan
Moore, R. E. (1979): Methods and applications of interval analysis.SIAM. doi:10.1137/1.9781611970906. Smarandache, F (2022):Neutrosophic Statistics is an extension of Interval Statistics, while Plithogenic Statistics is the most general form of statistics(second version).Internation journal of neutrosophic science. 19(1),pp.148-165. doi:10.54216/IJNS.190111
#Division of neutrosopic numbers x=list(c(8,4),c(2,4)) interval_div(x)#Division of neutrosopic numbers x=list(c(8,4),c(2,4)) interval_div(x)
Interval multiplication of the neutrosophic numbers
interval_mul(data)interval_mul(data)
data |
List of neutrosophic numbers.This numeric list contains at least two neutrosophic intervals. Each interval value should contains two elements, lower and upper.If it crisp value is used,it is considered as an interval with same upper and lower value. |
A numeric vector of length 2,indicating a product value of neutrosophic intervals
Zahid Khan
Moore, R. E. (1979): Methods and applications of interval analysis.SIAM. doi:10.1137/1.9781611970906. Smarandache, F (2022):Neutrosophic Statistics is an extension of Interval Statistics, while Plithogenic Statistics is the most general form of statistics(second version).Internation journal of neutrosophic science. 19(1),pp.148-165. doi:10.54216/IJNS.190111
#Multiplication of the neutrosopic numbers x=list(c(2,5),c(7,8)) interval_mul(x)#Multiplication of the neutrosopic numbers x=list(c(2,5),c(7,8)) interval_mul(x)
Sorting of neutrosophic values in the ascending order
interval_sort(data)interval_sort(data)
data |
data is a list of neutrosophic numbers |
List of intervals in asceding order.
Zahid Khan
Moore, R. E. (1979): Methods and applications of interval analysis.SIAM. doi:10.1137/1.9781611970906
data <- list(c(5, 10), c(4,6), c(2, 3)) sort <- interval_sort(data) print(sort)data <- list(c(5, 10), c(4,6), c(2, 3)) sort <- interval_sort(data) print(sort)
Interval subtraction of neutrosophic numbers.
interval_sub(data)interval_sub(data)
data |
List of neutrosophic numbers.This numeric list contains at least two neutrosophic intervals. Each interval value should contains two elements, lower and upper.If it crisp value is used,it is considered as an interval with same upper and lower value. |
A numeric vector of length 2,indicating a substracted value of neutrosophic intervals
Zahid Khan
Moore, R. E. (1979): Methods and applications of interval analysis.SIAM. doi:10.1137/1.9781611970906
Smarandache, F (2022):Neutrosophic Statistics is an extension of Interval Statistics, while Plithogenic Statistics is the most general form of statistics(second version).Internation journal of neutrosophic science. 19(1),pp.148-165. doi:10.54216/IJNS.190111.
#Substraction of two neutrosopic numbers x=list(c(10,15),c(5,10)) interval_sub(x)#Substraction of two neutrosopic numbers x=list(c(10,15),c(5,10)) interval_sub(x)
Neutrosophic coefficient of variation is an interval value of the neutrosphic numbers
ncv(data)ncv(data)
data |
data is a list of neutrosophic numbers |
Interval cv value.
Zahid Khan
Florentin Smarandache (2014): Introduction to Neutrosophic Statistics. ISBN: 9781599732749 Hussein Al-Marshadi, Ali and Aslam, Muhammad and Abdullah, Alharbey (2021): Uncertainty-Based Trimmed Coefficient of Variation with Application, Journal of Mathematics, 2021(1), pages 5511904. Wiley Online Library. doi:10.1155/2021/5511904
Kandemir, Hacer Şengül and Aral, Nazlım Deniz and Karakaş, Murat and Et, Mikail (2024): Neutrosophic Statistical Analysis of Temperatures of Cities in the Southeastern Anatolia Region of Turkey, Neutrosophic Systems with Applications, 14, pp. 50-59. doi:10.61356/j.nswa.2024.119
data <- list(c(1, 2), c(4), c(2, 3)) mean <- nmean(data) print(mean)data <- list(c(1, 2), c(4), c(2, 3)) mean <- nmean(data) print(mean)
Computes various properties of the Neutrosophic Exponential distribution, including its density, cumulative distribution function (CDF), quantiles,random numbers with summary statistics,PDF and CDF plots of the distribution.
dnexp(x, rate_l, rate_u) pnexp(q, rate_l, rate_u) qnexp(p, rate_l, rate_u) rnexp(n, rate_l, rate_u, stats=FALSE) plot_npdfexp(rate_l, rate_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "PDF Neutrosophic Exponential Distribution", x.label = "x", y.label = "Density") plot_ncdfexp(rate_l, rate_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "CDF Neutrosophic Exponential Distribution", x.label = "x", y.label = "Cumulative Probability")dnexp(x, rate_l, rate_u) pnexp(q, rate_l, rate_u) qnexp(p, rate_l, rate_u) rnexp(n, rate_l, rate_u, stats=FALSE) plot_npdfexp(rate_l, rate_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "PDF Neutrosophic Exponential Distribution", x.label = "x", y.label = "Density") plot_ncdfexp(rate_l, rate_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "CDF Neutrosophic Exponential Distribution", x.label = "x", y.label = "Cumulative Probability")
x |
A numeric vector of observations for which the function will compute the corresponding distribution values. |
n |
number of random generated values |
rate_l |
A positive numeric value representing the lower bound of the rate parameter of the Neutrosophic Exponential distribution. |
rate_u |
A positive numeric value representing the upper bound of the rate parameter of the Neutrosophic Exponential distribution. This must be greater than or equal to |
p |
A vector of probabilities for which the function will compute the corresponding quantile values |
q |
A vector of quantiles for which the function will compute the corresponding CDF values |
stats |
Logical; if |
color.fill |
A string representing the color for neutrosophic region. |
color.line |
A string representing the color used for the line of the PDF or CDF in the plots. |
title |
A string representing the title of the plot. |
x.label |
A string representing the label for the x-axis. |
y.label |
A string representing the label for the y-axis. |
The function computes various properties of the Neutrosophic Exponential distribution. Depending on the function variant used (e.g., density, CDF, quantiles), it will return the corresponding statistical measure for each input value of x in case of random number generation from Neutrosophic Exponential distribution. Moreover basic plots of PDF and CDF can be visualized.
dnexp returns the PDF values
pnexp returns the lower tail CDF values.
qnexp returns the quantile values
rnexp return random values with summary statistics of the simulated data
plot_npdfexp returns PDF plot at given values of rate parameter
plot_ncdfexp returns CDF plot at given values of rate parameter
Zahid Khan
Duan, W., Q., Khan, Z., Gulistan, M., Khurshid, A. (2021). Neutrosophic Exponential Distribution: Modeling and Applications for Complex Data Analysis, Complexity, 2021, 1-8.doi:10.1155/2021/5970613
# random number with summary statistics rnexp(10, rate_l=2, rate_u=4, stats = TRUE) # PDF values x <- c(1, 2, 3) # Values at which to evaluate the PDF rate_l <- 0.5 rate_u <- 2.0 dnexp(x, rate_l, rate_u) # CDF values q <- c(2, 3, 3.5) rate_l <- 0.5 rate_u <- 2.0 pnexp(q, rate_l, rate_u) # Quantile values p <- 0.5 # Probability at which to evaluate the quantile rate_l <- 0.5 rate_u <- 2.0 qnexp(p, rate_l, rate_u) # PDF PLOT plot_npdfexp(rate_l = 1, rate_u = 2, x = c(0, 5)) # CDF PLOT plot_ncdfexp(rate_l = 1, rate_u = 2, x = c(0, 5))# random number with summary statistics rnexp(10, rate_l=2, rate_u=4, stats = TRUE) # PDF values x <- c(1, 2, 3) # Values at which to evaluate the PDF rate_l <- 0.5 rate_u <- 2.0 dnexp(x, rate_l, rate_u) # CDF values q <- c(2, 3, 3.5) rate_l <- 0.5 rate_u <- 2.0 pnexp(q, rate_l, rate_u) # Quantile values p <- 0.5 # Probability at which to evaluate the quantile rate_l <- 0.5 rate_u <- 2.0 qnexp(p, rate_l, rate_u) # PDF PLOT plot_npdfexp(rate_l = 1, rate_u = 2, x = c(0, 5)) # CDF PLOT plot_ncdfexp(rate_l = 1, rate_u = 2, x = c(0, 5))
Computes various properties of the Neutrosophic Gamma distribution, including its density, cumulative distribution function (CDF), quantiles,random numbers with summary statistics,PDF and CDF plots of the distribution.
dngam(x, scale_l, scale_u, shape_l, shape_u) pngam(q, scale_l, scale_u, shape_l, shape_u) qngam(p, scale_l, scale_u, shape_l, shape_u) rngam(n, scale_l, scale_u, shape_l, shape_u, stats = FALSE) plot_npdfgam(scale_l, scale_u, shape_l, shape_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "PDF Neutrosophic Gamma Distribution", x.label = "x", y.label = "Density") plot_ncdfgam(scale_l, scale_u, shape_l, shape_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "CDF Neutrosophic Gamma Distribution", x.label = "x", y.label = "Cumulative Probability")dngam(x, scale_l, scale_u, shape_l, shape_u) pngam(q, scale_l, scale_u, shape_l, shape_u) qngam(p, scale_l, scale_u, shape_l, shape_u) rngam(n, scale_l, scale_u, shape_l, shape_u, stats = FALSE) plot_npdfgam(scale_l, scale_u, shape_l, shape_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "PDF Neutrosophic Gamma Distribution", x.label = "x", y.label = "Density") plot_ncdfgam(scale_l, scale_u, shape_l, shape_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "CDF Neutrosophic Gamma Distribution", x.label = "x", y.label = "Cumulative Probability")
x |
A numeric vector of observations for which the function will compute the corresponding distribution values. |
n |
number of random generated values |
scale_l |
A positive numeric value representing the lower bound of the scale parameter of the Neutrosophic Gamma distribution. |
scale_u |
A positive numeric value representing the upper bound of the scale parameter of the Neutrosophic Gamma distribution. This must be greater than or equal to |
shape_l |
A positive numeric value representing the lower bound of the shape parameter of the Neutrosophic Gamma distribution. |
shape_u |
A positive numeric value representing the upper bound of the shape parameter of the Neutrosophic Gamma distribution. |
p |
A vector of probabilities for which the function will compute the corresponding quantile values |
q |
A vector of quantiles for which the function will compute the corresponding CDF values |
stats |
Logical; if |
color.fill |
A string representing the color for neutrosophic region. |
color.line |
A string representing the color used for the line of the PDF or CDF in the plots. |
title |
A string representing the title of the plot. |
x.label |
A string representing the label for the x-axis. |
y.label |
A string representing the label for the y-axis. |
The function computes various properties of the Neutrosophic Gamma distribution. Depending on the function variant used (e.g., density, CDF, quantiles), it will return the corresponding statistical measure for each input value of x in case of random number generation from Neutrosophic Gamma distribution. Moreover basic plots of PDF and CDF can be visualized.
dngam returns the PDF values
pngam returns the lower tail CDF values.
qngam returns the quantile values
rngam return random values with summary statistics of the simulated data
plot_npdfgam returns PDF plot at given values of distributional parameters
plot_ncdfgam returns CDF plot at given values of distributional parameters
Zahid Khan
Khan Z, Al-Bossly A, Almazah M, Alduais FS. (2021). On Statistical Development of Neutrosophic Gamma Distribution with Applications to Complex Data Analysis, Complexity, 2021, 1-8.doi:10.1155/2021/3701236
# random number Generation with summary statistics rngam(10, scale_l = 2, scale_u = 4, shape_l = 1, shape_u = 1, stats = TRUE) # PDF values x <- 2 scale_l <- 1 scale_u <- 2.0 shape_l<-0.5 shape_u<-2 dngam(x, scale_l, scale_u, shape_l, shape_u) # CDF values q <- 1.5 scale_l <- 1 scale_u <- 2.0 shape_l<-0.5 shape_u<-2.0 pngam(q, scale_l, scale_u, shape_l, shape_u) # Quantile values p <- 0.5 scale_l <- 1 scale_u <- 2.0 shape_l<-0.5 shape_u<-2 qngam(p, scale_l, scale_u, shape_l, shape_u) # PDF PLOT scale_l <- 1 scale_u <- 1 shape_l<-2 shape_u<-3 plot_npdfgam(scale_l, scale_u, shape_l, shape_u, x = c(0, 5)) # CDF PLOT scale_l <- 1 scale_u <- 1 shape_l<-2 shape_u<-3 plot_ncdfgam(scale_l, scale_u, shape_l, shape_u, x = c(0, 5))# random number Generation with summary statistics rngam(10, scale_l = 2, scale_u = 4, shape_l = 1, shape_u = 1, stats = TRUE) # PDF values x <- 2 scale_l <- 1 scale_u <- 2.0 shape_l<-0.5 shape_u<-2 dngam(x, scale_l, scale_u, shape_l, shape_u) # CDF values q <- 1.5 scale_l <- 1 scale_u <- 2.0 shape_l<-0.5 shape_u<-2.0 pngam(q, scale_l, scale_u, shape_l, shape_u) # Quantile values p <- 0.5 scale_l <- 1 scale_u <- 2.0 shape_l<-0.5 shape_u<-2 qngam(p, scale_l, scale_u, shape_l, shape_u) # PDF PLOT scale_l <- 1 scale_u <- 1 shape_l<-2 shape_u<-3 plot_npdfgam(scale_l, scale_u, shape_l, shape_u, x = c(0, 5)) # CDF PLOT scale_l <- 1 scale_u <- 1 shape_l<-2 shape_u<-3 plot_ncdfgam(scale_l, scale_u, shape_l, shape_u, x = c(0, 5))
Neutrosophic kurtosis is an interval value that measures the flatness and peakedness of neutrosophic data using the method of moments
nkur(data)nkur(data)
data |
data is a list of neutrosophic numbers |
An interval value of coefficeint of Kurtosis.
Zahid Khan
Florentin Smarandache (2014): Introduction to Neutrosophic Statistics. ISBN: 9781599732749
Aslam, Muhammad (2021): A study on skewness and kurtosis estimators of wind speed distribution under indeterminacy, Theoretical and Applied Climatology, 143(3), pp. 1227-1234. doi:10.1007/s00704-020-03509-5
nsk.
data <- list(c(1, 2), c(4), c(2, 3),c(6,8),c(12,20),c(20,30)) k <- nkur(data) print(k)data <- list(c(1, 2), c(4), c(2, 3),c(6,8),c(12,20),c(20,30)) k <- nkur(data) print(k)
Computes various properties of the Neutrosophic Laplace distribution, including its density, cumulative distribution function (CDF), quantiles,random numbers with summary statistics,PDF and CDF plots of the distribution.
dnlap(x, scale_l, scale_u, location_l, location_u) pnlap(q, scale_l, scale_u, location_l, location_u) qnlap(p, scale_l, scale_u, location_l, location_u) rnlap(n, scale_l, scale_u, location_l, location_u, stats = FALSE) plot_npdflap(scale_l, scale_u, location_l, location_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "PDF Neutrosophic Laplace Distribution", x.label = "x", y.label = "Density") plot_ncdflap(scale_l, scale_u, location_l, location_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "CDF Neutrosophic Laplace Distribution", x.label = "x", y.label = "Cumulative Probability")dnlap(x, scale_l, scale_u, location_l, location_u) pnlap(q, scale_l, scale_u, location_l, location_u) qnlap(p, scale_l, scale_u, location_l, location_u) rnlap(n, scale_l, scale_u, location_l, location_u, stats = FALSE) plot_npdflap(scale_l, scale_u, location_l, location_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "PDF Neutrosophic Laplace Distribution", x.label = "x", y.label = "Density") plot_ncdflap(scale_l, scale_u, location_l, location_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "CDF Neutrosophic Laplace Distribution", x.label = "x", y.label = "Cumulative Probability")
x |
A numeric vector of observations for which the function will compute the corresponding distribution values. |
n |
number of random generated values |
scale_l |
A positive numeric value representing the lower bound of the scale parameter of the Neutrosophic Laplace distribution. |
scale_u |
A positive numeric value representing the upper bound of the scale parameter of the Neutrosophic Laplace distribution. This must be greater than or equal to |
location_l |
A positive numeric value representing the lower bound of the location parameter of the Neutrosophic Laplace distribution. |
location_u |
A positive numeric value representing the upper bound of the location parameter of the Neutrosophic Laplace distribution. |
p |
A vector of probabilities for which the function will compute the corresponding quantile values |
q |
A vector of quantiles for which the function will compute the corresponding CDF values |
stats |
Logical; if |
color.fill |
A string representing the color for neutrosophic region. |
color.line |
A string representing the color used for the line of the PDF or CDF in the plots. |
title |
A string representing the title of the plot. |
x.label |
A string representing the label for the x-axis. |
y.label |
A string representing the label for the y-axis. |
The function computes various properties of the Neutrosophic Laplace distribution. Depending on the function variant used (e.g., density, CDF, quantiles), it will return the corresponding statistical measure for each input value of x in case of random number generation from Neutrosophic Laplace distribution. Moreover basic plots of PDF and CDF can be visualized.
dnlap returns the PDF values
pnlap returns the lower tail CDF values.
qnlap returns the quantile values
rnlap return random values with summary statistics of the simulated data
plot_npdflap returns PDF plot at given values of distributional parameters
plot_ncdflap returns CDF plot at given values of distributional parameters
Zahid Khan
Musa A, Khan Z. (2024). Neutrosophic Laplace Distribution with Properties and Applications in Decision Making. International Journal of Neutrosophic Science, 2024, 73-84. doi:10.54216/IJNS.230106.
# random number Generation with summary statistics rnlap(10, scale_l = 2, scale_u = 4, location_l = 1, location_u = 1, stats = TRUE) # PDF values x <- 2 scale_l <- 0.5 scale_u <- 1 location_l<-0 location_u<-0 dnlap(x, scale_l, scale_u, location_l, location_u) # CDF values q <- 1.5 scale_l <- 1 scale_u <- 2 location_l<-0 location_u<-0 pnlap(q, scale_l, scale_u, location_l, location_u) # Quantile values p <- 0.1 scale_l <- 0.5 scale_u <- 0.7 location_l<-0 location_u<-0 qnlap(p, scale_l, scale_u, location_l, location_u) # PDF PLOT scale_l <- 0.5 scale_u <- 1 location_l<-0 location_u<-0 plot_npdflap(scale_l, scale_u, location_l, location_u, x = c(-5, 5)) # CDF PLOT scale_l <- 0.5 scale_u <- 1 location_l<-0 location_u<-0 plot_ncdflap(scale_l, scale_u, location_l, location_u, x = c(-5, 5))# random number Generation with summary statistics rnlap(10, scale_l = 2, scale_u = 4, location_l = 1, location_u = 1, stats = TRUE) # PDF values x <- 2 scale_l <- 0.5 scale_u <- 1 location_l<-0 location_u<-0 dnlap(x, scale_l, scale_u, location_l, location_u) # CDF values q <- 1.5 scale_l <- 1 scale_u <- 2 location_l<-0 location_u<-0 pnlap(q, scale_l, scale_u, location_l, location_u) # Quantile values p <- 0.1 scale_l <- 0.5 scale_u <- 0.7 location_l<-0 location_u<-0 qnlap(p, scale_l, scale_u, location_l, location_u) # PDF PLOT scale_l <- 0.5 scale_u <- 1 location_l<-0 location_u<-0 plot_npdflap(scale_l, scale_u, location_l, location_u, x = c(-5, 5)) # CDF PLOT scale_l <- 0.5 scale_u <- 1 location_l<-0 location_u<-0 plot_ncdflap(scale_l, scale_u, location_l, location_u, x = c(-5, 5))
Neutrosophic mean is an interval value of the neutrosphic numbers
nmean(data)nmean(data)
data |
data is a list of neutrosophic numbers |
Interval mean value.
Zahid Khan
Florentin Smarandache (2014): Introduction to Neutrosophic Statistics. ISBN: 9781599732749
data <- list(c(1, 2), c(4), c(2, 3)) mean <- nmean(data) print(mean)data <- list(c(1, 2), c(4), c(2, 3)) mean <- nmean(data) print(mean)
Finding the median of the neutrosophic interval values
nmedian(data)nmedian(data)
data |
list of neutrosophic numbers |
interval median value.
Zahid Khan
Florentin Smarandache (2014): Introduction to Neutrosophic Statistics. ISBN: 9781599732749
data <- list(c(5, 10), c(4,6), c(2, 3)) med <- nmedian(data) print(med)data <- list(c(5, 10), c(4,6), c(2, 3)) med <- nmedian(data) print(med)
Computes various properties of the Neutrosophic Normal distribution, including its density, cumulative distribution function (CDF), quantiles,random numbers with summary statistics,PDF and CDF plots of the distribution.
dnnorm(x, sd_l, sd_u, mean_l, mean_u) pnnorm(q, sd_l, sd_u, mean_l, mean_u) qnnorm(p, sd_l, sd_u, mean_l, mean_u) rnnorm(n, sd_l, sd_u, mean_l, mean_u, stats = FALSE) plot_npdfnorm(sd_l, sd_u, mean_l, mean_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "PDF Neutrosophic Normal Distribution", x.label = "x", y.label = "Density") plot_ncdfnorm(sd_l, sd_u, mean_l, mean_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "CDF Neutrosophic Normal Distribution", x.label = "x", y.label = "Cumulative Probability")dnnorm(x, sd_l, sd_u, mean_l, mean_u) pnnorm(q, sd_l, sd_u, mean_l, mean_u) qnnorm(p, sd_l, sd_u, mean_l, mean_u) rnnorm(n, sd_l, sd_u, mean_l, mean_u, stats = FALSE) plot_npdfnorm(sd_l, sd_u, mean_l, mean_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "PDF Neutrosophic Normal Distribution", x.label = "x", y.label = "Density") plot_ncdfnorm(sd_l, sd_u, mean_l, mean_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "CDF Neutrosophic Normal Distribution", x.label = "x", y.label = "Cumulative Probability")
x |
A numeric vector of observations for which the function will compute the corresponding distribution values. |
n |
number of random generated values |
sd_l |
A positive numeric value representing the lower bound of the sd parameter of the Neutrosophic Normal distribution. |
sd_u |
A positive numeric value representing the upper bound of the sd parameter of the Neutrosophic Normal distribution. This must be greater than or equal to |
mean_l |
A numeric value representing the lower bound of the mean parameter of the Neutrosophic Normal distribution. |
mean_u |
A numeric value representing the upper bound of the mean parameter of the Neutrosophic Normal distribution. |
p |
A vector of probabilities for which the function will compute the corresponding quantile values |
q |
A vector of quantiles for which the function will compute the corresponding CDF values |
stats |
Logical; if |
color.fill |
A string representing the color for neutrosophic region. |
color.line |
A string representing the color used for the line of the PDF or CDF in the plots. |
title |
A string representing the title of the plot. |
x.label |
A string representing the label for the x-axis. |
y.label |
A string representing the label for the y-axis. |
The function computes various properties of the Neutrosophic Normal distribution. Depending on the function variant used (e.g., density, CDF, quantiles), it will return the corresponding statistical measure for each input value of x in case of random number generation from Neutrosophic Normal distribution. Moreover basic plots of PDF and CDF can be visualized.
dnnorm returns the PDF values
pnnorm returns the lower tail CDF values.
qnnorm returns the quantile values
rnnorm return random values with summary statistics of the simulated data
plot_npdfnorm returns PDF plot at given values of distributional parameters
plot_ncdfnorm returns CDF plot at given values of distributional parameters
Zahid Khan
Patro SK, Smarandache F. (2016). The neutrosophic statistical distribution, more problems, more solutions. Neutrosophic Sets and Systems, 12, 73-79.doi:10.5281/zenodo.571153
# random number Generation with summary statistics rnnorm(10, sd_l = 2, sd_u = 4, mean_l = 1, mean_u = 1, stats = TRUE) # PDF values x <- 2 sd_l <- 0.5 sd_u <- 1 mean_l<-0 mean_u<-0 dnnorm(x, sd_l, sd_u, mean_l, mean_u) # CDF values q <- 1.5 sd_l <- 1 sd_u <- 2 mean_l<-0 mean_u<-0 pnnorm(q, sd_l, sd_u, mean_l, mean_u) # Quantile values p <- 0.1 sd_l <- 0.5 sd_u <- 0.7 mean_l<-0 mean_u<-0 qnnorm(p, sd_l, sd_u, mean_l, mean_u) # PDF PLOT sd_l <- 0.5 sd_u <- 1 mean_l<-0 mean_u<-0 plot_npdfnorm(sd_l, sd_u, mean_l, mean_u, x = c(-5, 5)) # CDF PLOT sd_l <- 0.5 sd_u <- 1 mean_l<-0 mean_u<-0 plot_ncdfnorm(sd_l, sd_u, mean_l, mean_u, x = c(-5, 5))# random number Generation with summary statistics rnnorm(10, sd_l = 2, sd_u = 4, mean_l = 1, mean_u = 1, stats = TRUE) # PDF values x <- 2 sd_l <- 0.5 sd_u <- 1 mean_l<-0 mean_u<-0 dnnorm(x, sd_l, sd_u, mean_l, mean_u) # CDF values q <- 1.5 sd_l <- 1 sd_u <- 2 mean_l<-0 mean_u<-0 pnnorm(q, sd_l, sd_u, mean_l, mean_u) # Quantile values p <- 0.1 sd_l <- 0.5 sd_u <- 0.7 mean_l<-0 mean_u<-0 qnnorm(p, sd_l, sd_u, mean_l, mean_u) # PDF PLOT sd_l <- 0.5 sd_u <- 1 mean_l<-0 mean_u<-0 plot_npdfnorm(sd_l, sd_u, mean_l, mean_u, x = c(-5, 5)) # CDF PLOT sd_l <- 0.5 sd_u <- 1 mean_l<-0 mean_u<-0 plot_ncdfnorm(sd_l, sd_u, mean_l, mean_u, x = c(-5, 5))
Neutrosophic quantiles provide three quantile interval values of the neutrosophic data
nquant(data)nquant(data)
data |
A list of neutrosophic numbers.Each neutrosophic number is represented by an interval. |
A named list containing the first, second and third quantile interval values where each quantile is represented as an interval value
Zahid Khan
Florentin Smarandache (2014): Introduction to Neutrosophic Statistics. ISBN: 9781599732749
data <- list(c(5, 10), c(4,6), c(2, 3),c(4,8)) q <- nquant(data) print(q)data <- list(c(5, 10), c(4,6), c(2, 3),c(4,8)) q <- nquant(data) print(q)
Computes various properties of the Neutrosophic Rayleigh distribution, including its density, cumulative distribution function (CDF), quantiles,random numbers with summary statistics,PDF and CDF plots of the distribution.
dnray(x, scale_l, scale_u) pnray(q, scale_l, scale_u) qnray(p, scale_l, scale_u) rnray(n, scale_l, scale_u, stats=FALSE) plot_npdfray(scale_l, scale_u, x = c(0, 5),color.fill = "lightblue", color.line = "blue", title = "PDF Neutrosophic Rayleigh Distribution", x.label = "x", y.label = "Density") plot_ncdfray(scale_l, scale_u, x = c(0, 5),color.fill = "lightblue", color.line = "blue", title = "CDF Neutrosophic Rayleigh Distribution", x.label = "x", y.label = "Cumulative Probability")dnray(x, scale_l, scale_u) pnray(q, scale_l, scale_u) qnray(p, scale_l, scale_u) rnray(n, scale_l, scale_u, stats=FALSE) plot_npdfray(scale_l, scale_u, x = c(0, 5),color.fill = "lightblue", color.line = "blue", title = "PDF Neutrosophic Rayleigh Distribution", x.label = "x", y.label = "Density") plot_ncdfray(scale_l, scale_u, x = c(0, 5),color.fill = "lightblue", color.line = "blue", title = "CDF Neutrosophic Rayleigh Distribution", x.label = "x", y.label = "Cumulative Probability")
x |
A numeric vector of observations for which the function will compute the corresponding distribution values. |
n |
number of random generated values |
scale_l |
A positive numeric value representing the lower bound of the scale parameter of the Neutrosophic Rayleigh distribution. |
scale_u |
A positive numeric value representing the upper bound of the scale parameter of the Neutrosophic Rayleigh distribution. This must be greater than or equal to |
p |
A vector of probabilities for which the function will compute the corresponding quantile values |
q |
A vector of quantiles for which the function will compute the corresponding CDF values |
stats |
Logical; if |
color.fill |
A string representing the color for neutrosophic region. |
color.line |
A string representing the color used for the line of the PDF or CDF in the plots. |
title |
A string representing the title of the plot. |
x.label |
A string representing the label for the x-axis. |
y.label |
A string representing the label for the y-axis. |
The function computes various properties of the Neutrosophic Rayleigh distribution. Depending on the function variant used (e.g., density, CDF, quantiles), it will return the corresponding statistical measure for each input value of x in case of random number generation from Neutrosophic Rayleigh distribution. Moreover basic plots of PDF and CDF can be visualized.
dnray returns the PDF values
pnray returns the lower tail CDF values
qnray returns the quantile values
rnray return random values with summary statistics of the simulated data
plot_npdfexp returns PDF plot at given values of scale parameter
plot_ncdfexp returns CDF plot at given values of scale parameter
Zahid Khan
Khan, Z., Gulistan, M., Kausar, N., Park, C. (2021). Neutrosophic Rayleigh Model With Some Basic Characteristics and Engineering Applications. IEEE Access, 9, 71277-71283. doi:10.1109/ACCESS.2021.3078150.
# random number with summary statistics rnray(10, scale_l=2, scale_u=4, stats = TRUE) # PDF values x <- c(1, 2, 3) # Values at which to evaluate the PDF scale_l <- 0.5 scale_u <- 2.0 dnray(x, scale_l, scale_u) # CDF values q <- c(2, 3, 3.5) scale_l <- 0.5 scale_u <- 2.0 pnray(q, scale_l, scale_u) # Quantile values p <- 0.5 # Probability at which to evaluate the quantile scale_l <- 0.5 scale_u <- 2.0 qnray(p, scale_l, scale_u) # PDF PLOT scale_l <- 0.5 # Minimum rate scale_u <- 2 # Maximum rate plot_npdfray(scale_l, scale_u, x = c(0, 3)) # CDF PLOT scale_l <- 0.5 # Minimum rate scale_u <- 2.0 # Maximum rate plot_ncdfray(scale_l, scale_u, x = c(0, 3),title = "")# random number with summary statistics rnray(10, scale_l=2, scale_u=4, stats = TRUE) # PDF values x <- c(1, 2, 3) # Values at which to evaluate the PDF scale_l <- 0.5 scale_u <- 2.0 dnray(x, scale_l, scale_u) # CDF values q <- c(2, 3, 3.5) scale_l <- 0.5 scale_u <- 2.0 pnray(q, scale_l, scale_u) # Quantile values p <- 0.5 # Probability at which to evaluate the quantile scale_l <- 0.5 scale_u <- 2.0 qnray(p, scale_l, scale_u) # PDF PLOT scale_l <- 0.5 # Minimum rate scale_u <- 2 # Maximum rate plot_npdfray(scale_l, scale_u, x = c(0, 3)) # CDF PLOT scale_l <- 0.5 # Minimum rate scale_u <- 2.0 # Maximum rate plot_ncdfray(scale_l, scale_u, x = c(0, 3),title = "")
Neutrosophic skewness is imprecise value that measures the asymmetery of neutrosophic data using the method of moments
nsk(data)nsk(data)
data |
data is a list of neutrosophic numbers |
An interval value of Pearson coefficeint of skewness.
Zahid Khan
Florentin Smarandache (2014): Introduction to Neutrosophic Statistics. ISBN: 9781599732749 Aslam, Muhammad (2021): A study on skewness and kurtosis estimators of wind speed distribution under indeterminacy, Theoretical and Applied Climatology, 143(3), pp. 1227-1234.doi:10.1007/s00704-020-03509-5
data <- list(c(1, 2), c(4), c(2, 3),c(6,8),c(12,20)) s <- nsk(data) print(s)data <- list(c(1, 2), c(4), c(2, 3),c(6,8),c(12,20)) s <- nsk(data) print(s)
Neutrosophic standard deviation is an interval value of the neutrosphic numbers
nstd(data)nstd(data)
data |
data is a list of neutrosophic numbers |
Interval dispersion value.
Zahid Khan
Florentin Smarandache (2014): Introduction to Neutrosophic Statistics. ISBN: 9781599732749
data <- list(6, c(2, 5), 30, c(18, 24)) sd <- nstd(data) print(sd)data <- list(6, c(2, 5), 30, c(18, 24)) sd <- nstd(data) print(sd)
Descriptive summary of the neutrosphic numbers
nsummary(data)nsummary(data)
data |
data is a list of neutrosophic numbers |
Data frame of descriptive neutrosophic statistics.
Zahid Khan
Florentin Smarandache (2014): Introduction to Neutrosophic Statistics. ISBN: 9781599732749
data <- list(c(1, 2), c(4), c(2, 3),c(5,11),c(4,8),c(20,25)) s <- nsummary(data) print(s)data <- list(c(1, 2), c(4), c(2, 3),c(5,11),c(4,8),c(20,25)) s <- nsummary(data) print(s)
Neutrosophic variance is an interval value of the neutrosphic numbers
nvar(data)nvar(data)
data |
data is a list of neutrosophic numbers |
Interval dispersion value.
Zahid Khan
Florentin Smarandache (2014): Introduction to Neutrosophic Statistics. ISBN: 9781599732749
data <- list(6, c(2, 5), 30, c(18, 24)) variance <- nvar(data) print(variance)data <- list(6, c(2, 5), 30, c(18, 24)) variance <- nvar(data) print(variance)
Computes various properties of the Neutrosophic Weibull distribution, including its density, cumulative distribution function (CDF), quantiles,random numbers with summary statistics,PDF and CDF plots of the distribution.
dnwbl(x, scale_l, scale_u, shape_l, shape_u) pnwbl(q, scale_l, scale_u, shape_l, shape_u) qnwbl(p, scale_l, scale_u, shape_l, shape_u) rnwbl(n, scale_l, scale_u, shape_l, shape_u, stats = FALSE) plot_npdfwbl(scale_l, scale_u, shape_l, shape_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "PDF Neutrosophic Weibull Distribution", x.label = "x", y.label = "Density") plot_ncdfwbl(scale_l, scale_u, shape_l, shape_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "CDF Neutrosophic Weibull Distribution", x.label = "x", y.label = "Cumulative Probability")dnwbl(x, scale_l, scale_u, shape_l, shape_u) pnwbl(q, scale_l, scale_u, shape_l, shape_u) qnwbl(p, scale_l, scale_u, shape_l, shape_u) rnwbl(n, scale_l, scale_u, shape_l, shape_u, stats = FALSE) plot_npdfwbl(scale_l, scale_u, shape_l, shape_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "PDF Neutrosophic Weibull Distribution", x.label = "x", y.label = "Density") plot_ncdfwbl(scale_l, scale_u, shape_l, shape_u, x = c(0, 5), color.fill = "lightblue", color.line = "blue", title = "CDF Neutrosophic Weibull Distribution", x.label = "x", y.label = "Cumulative Probability")
x |
A numeric vector of observations for which the function will compute the corresponding distribution values. |
n |
number of random generated values |
scale_l |
A positive numeric value representing the lower bound of the scale parameter of the Neutrosophic Weibull distribution. |
scale_u |
A positive numeric value representing the upper bound of the scale parameter of the Neutrosophic Weibull distribution. This must be greater than or equal to |
shape_l |
A positive numeric value representing the lower bound of the shape parameter of the Neutrosophic Weibull distribution. |
shape_u |
A positive numeric value representing the upper bound of the shape parameter of the Neutrosophic Weibull distribution. |
p |
A vector of probabilities for which the function will compute the corresponding quantile values |
q |
A vector of quantiles for which the function will compute the corresponding CDF values |
stats |
Logical; if |
color.fill |
A string representing the color for neutrosophic region. |
color.line |
A string representing the color used for the line of the PDF or CDF in the plots. |
title |
A string representing the title of the plot. |
x.label |
A string representing the label for the x-axis. |
y.label |
A string representing the label for the y-axis. |
The function computes various properties of the Neutrosophic Weibull distribution. Depending on the function variant used (e.g., density, CDF, quantiles), it will return the corresponding statistical measure for each input value of x in case of random number generation from Neutrosophic Weibull distribution. Moreover basic plots of PDF and CDF can be visualized.
dnwbl returns the PDF values
pnwbl returns the lower tail CDF values.
qnwbl returns the quantile values
rnwbl return random values with summary statistics of the simulated data
plot_npdfwbl returns PDF plot at given values of distributional parameters
plot_ncdfwbl returns CDF plot at given values of distributional parameters
Zahid Khan
Khan, Kahid; Gulistan, Muhammad; Lane-Krebs, Katrina; Salem, Sultan (2023). Neutrophasic Weibull model with applications to survival studies. CQUniversity, 25-42.doi:10.1016/B978-0-323-99456-9.00007-6
# random number Generation with summary statistics rnwbl(5, scale_l = 2, scale_u = 4, shape_l = 1, shape_u = 1, stats = TRUE) # PDF values x <- 2 scale_l <- 1 scale_u <- 2.0 shape_l<-0.5 shape_u<-2 dnwbl(x, scale_l, scale_u, shape_l, shape_u) # CDF values q <- 1.5 scale_l <- 1 scale_u <- 2.0 shape_l<-0.5 shape_u<-2.0 pnwbl(q, scale_l, scale_u, shape_l, shape_u) # Quantile values p <- 0.5 scale_l <- 1 scale_u <- 2.0 shape_l<-0.5 shape_u<-2 qnwbl(p, scale_l, scale_u, shape_l, shape_u) # PDF PLOT scale_l <- 1 scale_u <- 1 shape_l<-2 shape_u<-3 plot_npdfwbl(scale_l, scale_u, shape_l, shape_u, x = c(0, 5)) # CDF PLOT scale_l <- 1 scale_u <- 1 shape_l<-2 shape_u<-3 plot_ncdfwbl(scale_l, scale_u, shape_l, shape_u, x = c(0, 5))# random number Generation with summary statistics rnwbl(5, scale_l = 2, scale_u = 4, shape_l = 1, shape_u = 1, stats = TRUE) # PDF values x <- 2 scale_l <- 1 scale_u <- 2.0 shape_l<-0.5 shape_u<-2 dnwbl(x, scale_l, scale_u, shape_l, shape_u) # CDF values q <- 1.5 scale_l <- 1 scale_u <- 2.0 shape_l<-0.5 shape_u<-2.0 pnwbl(q, scale_l, scale_u, shape_l, shape_u) # Quantile values p <- 0.5 scale_l <- 1 scale_u <- 2.0 shape_l<-0.5 shape_u<-2 qnwbl(p, scale_l, scale_u, shape_l, shape_u) # PDF PLOT scale_l <- 1 scale_u <- 1 shape_l<-2 shape_u<-3 plot_npdfwbl(scale_l, scale_u, shape_l, shape_u, x = c(0, 5)) # CDF PLOT scale_l <- 1 scale_u <- 1 shape_l<-2 shape_u<-3 plot_ncdfwbl(scale_l, scale_u, shape_l, shape_u, x = c(0, 5))