# PSDistr

# 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]  0.72517973 -1.01417346 -0.72370296 -0.75046843  0.06487877 -0.44419240
    #>  [7] -0.71071506 -0.83404673 -0.65304340 -0.64328024

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]  1.47602943  0.66991776  1.12713501 -0.44664731 -0.03431171  0.04385142
    #>  [7]  0.16737191  1.56040034  0.93300919  0.36102845

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] -0.2854987 -0.4723621  0.2676492  0.5063099 -0.6198623  1.7077907
    #>  [7]  2.3979575  1.9180331 -0.9669992  0.7317598

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] -0.7246533 -1.4880502  1.2629622  0.6284114  2.8143602 -0.3916846
    #>  [7] -1.0634502 -1.5890172  3.5892774  2.9038329

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] -0.71518822 -0.57696760  0.08840183 -0.47645229 -1.12528024 -0.85722703
    #>  [7] -0.94428720 -0.25766443 -0.55227331 -0.84850524

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]  0.278406720  1.556517872 -0.101838266  0.428527316  1.645365458
    #>  [6]  1.836425555  0.110333370  0.649998077  0.004952715  1.530213047