Distributions Derived from Normal Distribution.

PSDistr - Distributions Derived from Normal Distribution

author: Piotr Sulewski, Pomeranian University

Distributions derived from normal distribution are: two-piece power normal (TPPN), plasticizing component (PC), DS normal (DSN), expnormal (EN), Sulewski plasticizing component (SPC), easily changeable kurtosis (ECK) distributions. Density, distribution function, quantile function and random generation are presented. To read more about the package please see (and cite :)) papers:

1. Sulewski P. (2021) DS Normal Distribution: properties and applications, Lobachevskii Journal of Mathematics, 42(12), 2980-2999.
2. Sulewski P. (2022) Easily Changeable Kurtosis Distribution. Austrian Journal of Statistics, 52, 1-24.
3. Sulewski , P. (2022). New Members of The Johnson Family of Probability Distributions: Properties and Application, Accepted: February 2022. REVSTAT-Statistical Journal.
4. Sulewski P. (2020) Normal Distribution with Plasticizing Component, Communications in Statistics ? Theory and Method, 51(11), 3806-3835.
5. Sulewski P., Volodin A. (2022) Sulewski Plasticizing Component Distribution: properties and applications. Lobachtetavskii Journal of Mathtetamatics, 43(8), 2286-2300.
6. Sulewski P. (2021) Two-Piece Power Normal Distribution, Communications in Statistics ? Theory and Method, 50(11), 2619-2639.

Installation

You can install the released version of PSDistr from CRAN with:

install.packages("PSDistr")

You can install the development version of PSDistr from GitHub with:

library("remotes")
install_github("PiotrSule/PSDistr")

Functions

ddsn, pdsn, qdsn, rdsn

Density, distribution function, quantile function and random generation for the DS Normal Distribution are calculated

library(PSDistr)
ddsn(-0.5,2,2,2,0)
#> [1] 1.053981
pdsn(-0.5,2,2,2,0)
#> [1] 0.7733726
qdsn(0.5,2,2,2,0)
#> [1] -0.6823278
rdsn(10,2,2,2,0)
#>  [1] -0.9174543 -0.9531677 -0.9434789 -0.9387052 -0.7463924 -0.3198462
#>  [7] -0.5119604 -0.7520390 -0.5192255 -0.1585803

deck, peck, qeck, reck

Density, distribution function, quantile function and random generation for the Easily Changeable Kurtosis Distribution are calculated

deck(1,2,3)
#> [1] 0.2307129
peck(1,2,3)
#> [1] 0.9294434
qeck(0.5,2,3)
#> [1] 0
reck(10,2,3)
#>  [1]  0.19273161  0.29262681  0.26832902 -1.04825437 -1.55783427 -1.19081611
#>  [7]  0.03379742 -0.44629456 -0.59413517  0.72587502

den, pen, qen, ren

Density, distribution function, quantile function and random generation for the Expnormal Distribution are calculated

den(1,1,2,2,2,1)
#> [1] 0.2666153
pen(1,1,2,2,2,1)
#> [1] 0.7279188
qen(0.5,1,2,2,2,1)
#> [1] 0.2909696
ren(10,1,2,2,2,1)
#>  [1] -0.565035585  0.371245691  0.007892049  0.035879908  0.507669393
#>  [6] -0.242076982 -1.066860331  0.801121683 -0.353035247 -0.332387666

dpc, ppc, qpc, rpc

Density, distribution function, quantile function and random generation for the Plasticizing Component are calculated

dpc(0,1,2,2)
#> [1] 0.1933341
ppc(0,1,2,2)
#> [1] 0.4012937
qpc(0.5,1,2,2)
#> [1] 1
rpc(10,1,2,2)
#>  [1] -0.5623307  3.2750871 -0.3884369 -1.4182320 -1.1450447  3.8902870
#>  [7] -0.4963983 -0.4527041  0.3387212 -1.0823312

dspc, pspc, qspc, rspc

Density, distribution function, quantile function and random generation for the Sulewski Plasticizing Component Distribution are calculated

dspc(0,1,1,1,1,0)
#> [1] 0.2419707
pspc(0,1,1,1,1,0)
#> [1] 0.8413447
qspc(0.5,1,1,1,1,0)
#> [1] -0.6823278
rspc(10,1,1,1,1,0)
#>  [1] -0.79434037  0.01560102 -0.82784459  0.09298656 -1.18855183 -0.72773510
#>  [7] -0.43819889 -0.68688316 -0.61121603 -0.49309748

dspc, pspc, qspc, rspc

Density, distribution function, quantile function and random generation for the Two-piece Power Normal distribution are calculated

dtppn(2,1,1,1,2)
#> [1] 0.4839414
ptppn(2,1,1,1,2)
#> [1] 0.8413447
qtppn(0.5,1,1,1,2)
#> [1] 1
rtppn(10,1,1,1,2)
#>  [1]  1.8747816  0.2496032  0.1118770  0.5042015  0.9287008  0.3041738
#>  [7]  1.6097886 -0.2114342  1.9926648  0.6559251