Selection of an appropriate distribution using Propagate package in R
Dr. Zulfiqar Ali (Assistant Professor of Statistics, College of Statistical Sciences, University of the Punjab Lahore: Pakistan, Email: zulfiqar.stat@pu.edu.pk)
2022-10-20
This work describes the procedure of selecting an approriate probability distribution of any variable uisng Propagate package in R
The propagate package can be install and call in R or RStudio using the following commands
##install.packages("propagate")
library(propagate)## Warning: package 'propagate' was built under R version 4.1.2## Loading required package: MASS## Loading required package: tmvtnorm## Warning: package 'tmvtnorm' was built under R version 4.1.2## Loading required package: mvtnorm## Loading required package: Matrix## Loading required package: stats4## Loading required package: gmm## Warning: package 'gmm' was built under R version 4.1.2## Loading required package: sandwich## Warning: package 'sandwich' was built under R version 4.1.2## Loading required package: Rcpp## Warning: package 'Rcpp' was built under R version 4.1.2## Loading required package: ff## Warning: package 'ff' was built under R version 4.1.2## Loading required package: bit## Warning: package 'bit' was built under R version 4.1.2##
## Attaching package: 'bit'## The following object is masked from 'package:base':
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## xor## Attaching package ff## - getOption("fftempdir")=="C:/Users/DR9C3F~1.ZUL/AppData/Local/Temp/RtmpCCzjGg/ff"## - getOption("ffextension")=="ff"## - getOption("ffdrop")==TRUE## - getOption("fffinonexit")==TRUE## - getOption("ffpagesize")==65536## - getOption("ffcaching")=="mmnoflush" -- consider "ffeachflush" if your system stalls on large writes## - getOption("ffbatchbytes")==16777216 -- consider a different value for tuning your system## - getOption("ffmaxbytes")==536870912 -- consider a different value for tuning your system##
## Attaching package: 'ff'## The following objects are masked from 'package:utils':
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## write.csv, write.csv2## The following objects are masked from 'package:base':
##
## is.factor, is.ordered## Loading required package: minpack.lm## Warning: package 'minpack.lm' was built under R version 4.1.2Let generate a random vector of numerical values. Here, I will generate the vector from normal distribution
x=rnorm(10000,0,1)Let check the histogram of x.
hist(x)
Let
search an appropriate probability distribution on x using
fitDistr command.
g=fitDistr(x)## 1 of 32: Fitting Normal distribution...## .........## 2 of 32: Fitting Skewed-normal distribution...## .........10.........20.......## 3 of 32: Fitting Generalized normal distribution...## .........10.........20.......## 4 of 32: Fitting Log-normal distribution...## .........## 5 of 32: Fitting Scaled/shifted t- distribution...## .........10.........20.......## 6 of 32: Fitting Logistic distribution...## .........## 7 of 32: Fitting Uniform distribution...## .........## 8 of 32: Fitting Triangular distribution...## .........10.........20.......## 9 of 32: Fitting Trapezoidal distribution...## .........10.........20.........30.........40.........50
## .........60.........70.........80.## 10 of 32: Fitting Curvilinear Trapezoidal distribution...## .........10.........20.......## 11 of 32: Fitting Gamma distribution...## .........## 12 of 32: Fitting Inverse Gamma distribution...## .........## 13 of 32: Fitting Cauchy distribution...## .........## 14 of 32: Fitting Laplace distribution...## .........## 15 of 32: Fitting Gumbel distribution...## .........## 16 of 32: Fitting Johnson SU distribution...## .........10.........20.........30.........40.........50
## .........60.........70.........80.## 17 of 32: Fitting Johnson SB distribution...## .........10.........20.........30.........40.........50
## .........60.........70.........80.## 18 of 32: Fitting 3P Weibull distribution...## .........10.........20.......## 19 of 32: Fitting 2P Beta distribution...## .........## 20 of 32: Fitting 4P Beta distribution...## .........10.........20.........30.........40.........50
## .........60.........70.........80.## 21 of 32: Fitting Arcsine distribution...## .........## 22 of 32: Fitting von Mises distribution...## .........## 23 of 32: Fitting Inverse Gaussian distribution...## .........## 24 of 32: Fitting Generalized Extreme Value distribution...## .........10.........20.......## 25 of 32: Fitting Rayleigh distribution...## .........## 26 of 32: Fitting Chi-Square distribution...## ...## 27 of 32: Fitting Exponential distribution...## ...## 28 of 32: Fitting F- distribution...## .........## 29 of 32: Fitting Burr distribution...## ...## 30 of 32: Fitting Chi distribution...## ...## 31 of 32: Fitting Inverse Chi-Square distribution...## ...## 32 of 32: Fitting Cosine distribution...## .........
You can can see that the selected probability distribution is normal having minim value of BIC. Toc check the BIC of other probability function, we will use the following command.
##BIC values
fitDistr(x,plot="qq")$stat## 1 of 32: Fitting Normal distribution...## .........## 2 of 32: Fitting Skewed-normal distribution...## .........10.........20.......## 3 of 32: Fitting Generalized normal distribution...## .........10.........20.......## 4 of 32: Fitting Log-normal distribution...## .........## 5 of 32: Fitting Scaled/shifted t- distribution...## .........10.........20.......## 6 of 32: Fitting Logistic distribution...## .........## 7 of 32: Fitting Uniform distribution...## .........## 8 of 32: Fitting Triangular distribution...## .........10.........20.......## 9 of 32: Fitting Trapezoidal distribution...## .........10.........20.........30.........40.........50
## .........60.........70.........80.## 10 of 32: Fitting Curvilinear Trapezoidal distribution...## .........10.........20.......## 11 of 32: Fitting Gamma distribution...## .........## 12 of 32: Fitting Inverse Gamma distribution...## .........## 13 of 32: Fitting Cauchy distribution...## .........## 14 of 32: Fitting Laplace distribution...## .........## 15 of 32: Fitting Gumbel distribution...## .........## 16 of 32: Fitting Johnson SU distribution...## .........10.........20.........30.........40.........50
## .........60.........70.........80.## 17 of 32: Fitting Johnson SB distribution...## .........10.........20.........30.........40.........50
## .........60.........70.........80.## 18 of 32: Fitting 3P Weibull distribution...## .........10.........20.......## 19 of 32: Fitting 2P Beta distribution...## .........## 20 of 32: Fitting 4P Beta distribution...## .........10.........20.........30.........40.........50
## .........60.........70.........80.## 21 of 32: Fitting Arcsine distribution...## .........## 22 of 32: Fitting von Mises distribution...## .........## 23 of 32: Fitting Inverse Gaussian distribution...## .........## 24 of 32: Fitting Generalized Extreme Value distribution...## .........10.........20.......## 25 of 32: Fitting Rayleigh distribution...## .........## 26 of 32: Fitting Chi-Square distribution...## ...## 27 of 32: Fitting Exponential distribution...## ...## 28 of 32: Fitting F- distribution...## .........## 29 of 32: Fitting Burr distribution...## ...## 30 of 32: Fitting Chi distribution...## ...## 31 of 32: Fitting Inverse Chi-Square distribution...## ...## 32 of 32: Fitting Cosine distribution...## .........
## Distribution BIC RSS MSE
## 1 Normal -527.39993 3.489986e-07 0.0001343555
## 5 Scaled/shifted t- -526.39900 1.551563e-08 0.0001291922
## 2 Skewed-normal -522.97523 2.900305e-07 0.0001342590
## 3 Generalized normal -522.92366 3.296006e-07 0.0001343368
## 16 Johnson SU -522.00875 2.602955e-08 0.0001290495
## 17 Johnson SB -518.43249 3.305157e-07 0.0001343407
## 20 4P Beta -517.51207 4.271193e-07 0.0001357372
## 6 Logistic -507.15975 7.900709e-06 0.0001686637
## 18 3P Weibull -506.06375 1.000000e-06 0.0001623554
## 24 Generalized Extreme Value -502.93800 8.421501e-07 0.0001681587
## 22 von Mises -473.14195 1.000000e-06 0.0002471831
## 8 Triangular -472.04167 1.000000e-06 0.0002379494
## 9 Trapezoidal -467.65166 1.000000e-06 0.0002376859
## 15 Gumbel -369.73936 1.000000e-06 0.0007899394
## 14 Laplace -358.91588 1.180912e-04 0.0008920912
## 29 Burr -329.89035 9.035166e-05 0.0013000163
## 13 Cauchy -308.77174 2.431570e-04 0.0015671057
## 10 Curvilinear Trapezoidal -262.01018 1.000000e-06 0.0025198695
## 32 Cosine -259.55360 1.152761e-04 0.0027243867
## 25 Rayleigh -201.86862 2.661948e-02 0.0052090065
## 21 Arcsine -106.25709 1.348364e-02 0.0152514713
## 28 F- -98.01376 1.000000e-06 0.0167315760
## 4 Log-normal -95.91402 1.000000e-06 0.0171310102
## 12 Inverse Gamma -94.23611 1.000000e-06 0.0174570432
## 31 Inverse Chi-Square -90.27215 1.000000e-06 0.0191962743
## 11 Gamma -88.08844 1.000000e-06 0.0187055086
## 27 Exponential -86.42001 1.000000e-06 0.0200453791
## 26 Chi-Square -85.88550 1.000000e-06 0.0201661278
## 7 Uniform -78.75708 1.000000e-06 0.0207732245
## 19 2P Beta -72.90624 1.000000e-06 0.0221847380
## 23 Inverse Gaussian -53.68045 1.000000e-06 0.0275340854
## 30 Chi -49.93540 1.000000e-06 0.0302029032Note: This work is in progress.