Title: Distributions Derived from Normal Distribution
Version: 0.0.1
Description: Presentation of distributions such as: 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. For details on this method see: Sulewski (2019) <doi:10.1080/03610926.2019.1674871>, Sulewski (2021) <doi:10.1080/03610926.2020.1837881>, Sulewski (2021) <doi:10.1134/S1995080221120337>, Sulewski (2022) <"New members of the Johnson family of probability dis-tributions: properties and application">, Sulewski, Volodin (2022) <doi:10.1134/S1995080222110270>, Sulewski (2023) <doi:10.17713/ajs.v52i3.1434>.
Depends: R (≥ 3.5.0)
Imports: pracma
License: GPL-3
Language: en-US
Encoding: UTF-8
RoxygenNote: 7.2.3
Suggests: testthat (≥ 3.0.0), knitr, rmarkdown
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2023-09-12 17:11:48 UTC; piotr
Author: Piotr Sulewski ORCID iD [aut, cre]
Maintainer: Piotr Sulewski <piotr.sulewski@apsl.edu.pl>
Repository: CRAN
Date/Publication: 2023-09-13 09:50:05 UTC

The list of package functions and their demonstration

Description

The PSDistr presents the following distribution derived from the normal distribution: 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. The list of package functions is as follows:

Functions for the two-piece power normal distribution

dtppn

ptppn

qtppn

rtppn

Functions for the plasticizing component distribution

dpc

ppc

qpc

rpc

Functions for the DS normal distribution

ddsn

pdsn

qdsn

rdsn

#' @section Functions for the expnormal distribution:

den

pen

qen

ren

#' @section Functions for the Sulewski plasticizing component distribution:

dspc

pspc

qspc

rspc

#' @section Functions for the easily changeable kurtosis distribution:

deck

peck

qeck

reck

DS Normal Distribution

Description

Density, distribution function, quantile function and random generation for the DS normal distribution with parameters a, b, c and d.

Usage

ddsn(x, a, b, c, teta)

Arguments

x

real argument

a

non-negative multipurpose parameter and a+b>0

b

non-negative multipurpose parameter and a+b>0

c

real multipurpose parameter

teta

real position parameter

Details

Probability density function in Latex see formula (5) in the paper Cumulative distribution function in Latex see formula (6) Quantile function see formulas (8,9,10) Random number generator see Theorem (5)

Value

The function returns the value of the probability density function for the DS normal distribution

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian Uniwersity in Slupsk.

References

Sulewski P. (2021). DS Normal Distribution: properties and applications. Lobachevskii Journal of Mathematics 42(12), 2980-2999.

Examples

ddsn(-0.5,2,2,2,0)
pdsn(-0.5,2,2,2,0)
qdsn(0.5,2,2,2,0)
rdsn(10,2,2,2,0)

Easily Changeable Kurtosis Distribution

Description

Density, distribution function, quantile function and random generation for the Easily Changeable Kurtosis Distribution with parameters a and p.

Usage

deck(x, a, p)

Arguments

x

-a<x<a for -1<p<0 or -a<=x<=a for p>=1

a

positive scale parameter

p

shape parameter: p>-1

Details

Probability density function see formula (1) or (3) in the article Cumulative distribution function see formula (4) Quantile functon see formula (20) Random number generator see formula (41)

Value

The function returns the value of the probability density function for the Easily Changeable Kurtosis Distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2022). Easily Changeable Kurtosis Distribution. Austrian Journal of Statistics 52, 1-24.

Examples

deck(1,2,3)
peck(1,2,3)
qeck(0.5,2,3)
reck(10,2,3)

Expnormal Distribution

Description

Density, distribution function, quantile function and random generation for the Expnormal distribution with parameters a1, b1, a2, b2 and c.

Usage

den(x, a1, b1, a2, b2, c)

Arguments

x

real argument

a1

position parameter

b1

positive scale parameter

a2

position parameter

b2

positive scale parameter

c

semi-fraction parameter

Details

Probability density function see formula (2.1) in the article Cumulative distribution function see formula (2.3) Quantile functon see proposition (2.2) Random number generator see proposition (2.6)

Value

The function returns the value of the probability density function for the Expnormal distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2022). New Members of The Johnson Family of Probability Distributions:Properties and Application, Accepted: February 2022. REVSTAT-Statistical Journal.

Examples

den(1,1,2,2,2,1)
pen(1,1,2,2,2,1)
qen(0.5,1,2,2,2,1)
ren(10,1,2,2,2,1)

Plasticizing Component

Description

Density, distribution function, quantile function and random generation for the plasticizing component with parameters teta, s2 and c.

Usage

dpc(x, teta, s2, c)

Arguments

x

real argument

teta

position parameter

s2

positive scale parameter

c

shape parameter (c>=1)

Details

Probability density function see formula (2) in the article Cumulative distribution function see formula (4) Quantile functon see formula (9) Random number generator see formula (23)

Value

The function returns the value of the probability density function for the plasticizing component.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2020). Normal Distribution with Plasticizing Component, Communications in Statistics ? Theory and Method 51(11), 3806-3835.

Examples

dpc(0,1,2,2)
ppc(0,1,2,2)
qpc(0.5,1,2,2)
rpc(10,1,2,2)

Sulewski Plasticizing Component Distribution

Description

Density, distribution function, quantile function and random generation for the Sulewski plasticizing component distribution with parameters a, b, c, d and teta.

Usage

dspc(x, a, b, c, d, teta)

Arguments

x

real argument

a

multipurpose parameter (a>=0)

b

multipurpose parameter (b>=0, a+b>0)

c

multipurpose parameter

d

multipurpose parameter (d>=1)

teta

position parameter

Details

Probability density function see formula (2.1) in the article Cumulative distribution function see formula (2.2) Quantile functon see formulas (2.3-2.5) Random number generator see proposition (4)

Value

The function returns the value of the probability density function for the Sulewski plasticizing component distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P., Volodin, A. (2022). Sulewski Plasticizing Component Distribution: properties and applications. Lobachtetavskii Journal of Mathtetamatics 43(8), 2286-2300.

Examples

dspc(0,1,1,1,1,0)
pspc(0,1,1,1,1,0)
qspc(0.5,1,1,1,1,0)
rspc(10,1,1,1,1,0)

Two-Piece Power Normal Distribution

Description

Density, distribution function, quantile function and random generation for the two-piece power normal distribution with parameters teta, s1, s2 and c.

Usage

dtppn(x, teta, s1, s2, c)

Arguments

x

real argument

teta

position parameter

s1

positive scale parameter

s2

positive scale parameter

c

shape parameter (c>=1)

Details

Probability density function see formula (4) in the article Cumulative distribution function see formula (5) Quantile functon see formula (10) Random number generator see formula (21)

Value

The function returns the value of the probability density function for the two-piece power normal distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2021). Two-Piece Power Normal Distribution, Communications in Statistics - Theory and Method 50(11), 2619-2639.

Examples

dtppn(2,1,1,1,2)
ptppn(2,1,1,1,2)
qtppn(0.5,1,1,1,2)
rtppn(10,1,1,1,2)

DS Normal Distribution

Description

Density, distribution function, quantile function and random generation for the DS normal distribution with parameters a, b, c and d.

Usage

pdsn(x, a, b, c, teta)

Arguments

x

real argument

a

non-negative multipurpose parameter and a+b>0

b

non-negative multipurpose parameter and a+b>0

c

real multipurpose parameter

teta

real position parameter

Details

Probability density function in Latex see formula (5) in the paper Cumulative distribution function in Latex see formula (6) Quantile function see formulas (8,9,10) Random number generator see Theorem (5)

Value

The function returns the value of the cumulative distribution function for the DS normal distribution

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski P. (2021). DS Normal Distribution: properties and applications. Lobachevskii Journal of Mathematics 42(12), 2980-2999.

Examples

ddsn(-0.5,2,2,2,0)
pdsn(-0.5,2,2,2,0)
qdsn(0.5,2,2,2,0)
rdsn(10,2,2,2,0)

Easily Changeable Kurtosis Distribution

Description

Density, distribution function, quantile function and random generation for the Easily Changeable Kurtosis Distribution with parameters a and p.

Usage

peck(x, a, p)

Arguments

x

-a<x<a for -1<p<0 or -a<=x<=a for p>=1

a

positive scale parameter

p

shape parameter: p>-1

Details

Probability density function see formula (1) or (3) in the article Cumulative distribution function see formula (4) Quantile functon see formula (20) Random number generator see formula (41)

Value

The function returns the value of the cumulative distribution function for the Easily Changeable Kurtosis Distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2022). Easily Changeable Kurtosis Distribution. Austrian Journal of Statistics 52, 1-24.

Examples

deck(1,2,3)
peck(1,2,3)
qeck(0.5,2,3)
reck(10,2,3)

Expnormal Distribution

Description

Density, distribution function, quantile function and random generation for the Expnormal distribution with parameters a1, b1, a2, b2 and c.

Usage

pen(x, a1, b1, a2, b2, c)

Arguments

x

real argument

a1

position parameter

b1

positive scale parameter

a2

position parameter

b2

positive scale parameter

c

semi-fraction parameter

Details

Probability density function see formula (2.1) in the article Cumulative distribution function see formula (2.3) Quantile functon see proposition (2.2) Random number generator see proposition (2.6)

Value

The function returns the value of the cumulative distribution function for the Expnormal distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2022). New Members of The Johnson Family of Probability Distributions:Properties and Application, Accepted: February 2022. REVSTAT-Statistical Journal.

Examples

den(1,1,2,2,2,1)
pen(1,1,2,2,2,1)
qen(0.5,1,2,2,2,1)
ren(10,1,2,2,2,1)

Plasticizing Component

Description

Density, distribution function, quantile function and random generation for the plasticizing component with parameters teta, s2 and c.

Usage

ppc(x, teta, s2, c)

Arguments

x

real argument

teta

position parameter

s2

positive scale parameter

c

shape parameter (c>=1)

Details

Probability density function see formula (2) in the article Cumulative distribution function see formula (4) Quantile functon see formula (9) Random number generator see formula (23)

Value

The function returns the value of the cumulative distribution function for the plasticizing component.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2020). Normal Distribution with Plasticizing Component, Communications in Statistics ? Theory and Method 51(11), 3806-3835.

Examples

dpc(0,1,2,2)
ppc(0,1,2,2)
qpc(0.5,1,2,2)
rpc(10,1,2,2)

Sulewski Plasticizing Component Distribution

Description

Density, distribution function, quantile function and random generation for the Sulewski plasticizing component distribution with parameters a, b, c, d and teta.

Usage

pspc(x, a, b, c, d, teta)

Arguments

x

real argument

a

multipurpose parameter (a>=0)

b

multipurpose parameter (b>=0, a+b>0)

c

multipurpose parameter

d

multipurpose parameter (d>=1)

teta

position parameter

Details

Probability density function see formula (2.1) in the article Cumulative distribution function see formula (2.2) Quantile functon see formulas (2.3-2.5) Random number generator see proposition (4)

Value

The function returns the value of the cumulative distribution function for the Sulewski plasticizing component distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P., Volodin, A. (2022). Sulewski Plasticizing Component Distribution: properties and applications. Lobachtetavskii Journal of Mathtetamatics 43(8), 2286-2300.

Examples

dspc(0,1,1,1,1,0)
pspc(0,1,1,1,1,0)
qspc(0.5,1,1,1,1,0)
rspc(10,1,1,1,1,0)

Two-Piece Power Normal Distribution

Description

Density, distribution function, quantile function and random generation for the two-piece power normal distribution with parameters teta, s1, s2 and c.

Usage

ptppn(x, teta, s1, s2, c)

Arguments

x

real argument

teta

position parameter

s1

positive scale parameter

s2

positive scale parameter

c

shape parameter (c>=1)

Details

Probability density function see formula (4) in the article Cumulative distribution function see formula (5) Quantile functon see formula (10) Random number generator see formula (21)

Value

The function returns the value of the cumulative distribution function for the two-piece power normal distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2021). Two-Piece Power Normal Distribution, Communications in Statistics - Theory and Method 50(11), 2619-2639.

Examples

dtppn(2,1,1,1,2)
ptppn(2,1,1,1,2)
qtppn(0.5,1,1,1,2)
rtppn(10,1,1,1,2)

DS Normal Distribution

Description

Density, distribution function, quantile function and random generation for the DS normal distribution with parameters a, b, c and d.

Usage

qdsn(p, a, b, c, teta)

Arguments

p

probability between 0 and 1

a

non-negative multipurpose parameter and a+b>0

b

non-negative multipurpose parameter and a+b>0

c

real multipurpose parameter

teta

real position parameter

Details

Probability density function in Latex see formula (5) in the paper Cumulative distribution function in Latex see formula (6) Quantile function see formulas (8,9,10) Random number generator see Theorem (5)

Value

The function returns the value of the quantile function for the DS normal distribution

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski P. (2021). DS Normal Distribution: properties and applications. Lobachevskii Journal of Mathematics 42(12), 2980-2999.

Examples

ddsn(-0.5,2,2,2,0)
pdsn(-0.5,2,2,2,0)
qdsn(0.5,2,2,2,0)
rdsn(10,2,2,2,0)

Easily Changeable Kurtosis Distribution

Description

Density, distribution function, quantile function and random generation for the Easily Changeable Kurtosis Distribution with parameters a and p.

Usage

qeck(q, a, p)

Arguments

q

probability between 0 and 1

a

positive scale parameter

p

shape parameter: p>-1

Details

Probability density function see formula (1) or (3) in the article Cumulative distribution function see formula (4) Quantile functon see formula (20) Random number generator see formula (41)

Value

The function returns the value of the quantile function for the Easily Changeable Kurtosis Distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2022). Easily Changeable Kurtosis Distribution. Austrian Journal of Statistics 52, 1-24.

Examples

deck(1,2,3)
peck(1,2,3)
qeck(0.5,2,3)
reck(10,2,3)

Expnormal Distribution

Description

Density, distribution function, quantile function and random generation for the Expnormal distribution with parameters a1, b1, a2, b2 and c.

Usage

qen(p, a1, b1, a2, b2, c)

Arguments

p

probability between 0 and 1

a1

position parameter

b1

positive scale parameter

a2

position parameter

b2

positive scale parameter

c

semi-fraction parameter

Details

Probability density function see formula (2.1) in the article Cumulative distribution function see formula (2.3) Quantile functon see proposition (2.2) Random number generator see proposition (2.6)

Value

The function returns the value of the quantile function for the Expnormal distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2022). New Members of The Johnson Family of Probability Distributions:Properties and Application, Accepted: February 2022. REVSTAT-Statistical Journal.

Examples

den(1,1,2,2,2,1)
pen(1,1,2,2,2,1)
qen(0.5,1,2,2,2,1)
ren(10,1,2,2,2,1)

Plasticizing Component

Description

Density, distribution function, quantile function and random generation for the plasticizing component with parameters teta, s2 and c.

Usage

qpc(p, teta, s2, c)

Arguments

p

probability between 0 and 1

teta

position parameter

s2

positive scale parameter

c

shape parameter (c>=1)

Details

Probability density function see formula (2) in the article Cumulative distribution function see formula (4) Quantile functon see formula (9) Random number generator see formula (23)

Value

The function returns the value of the quantile function for the plasticizing component.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

SSulewski, P. (2020). Normal Distribution with Plasticizing Component, Communications in Statistics ? Theory and Method 51(11), 3806-3835.

Examples

dpc(0,1,2,2)
ppc(0,1,2,2)
qpc(0.5,1,2,2)
rpc(10,1,2,2)

Sulewski Plasticizing Component Distribution

Description

Density, distribution function, quantile function and random generation for the Sulewski plasticizing component distribution with parameters a, b, c, d and teta.

Usage

qspc(p, a, b, c, d, teta)

Arguments

p

probability between 0 and 1

a

multipurpose parameter (a>=0)

b

multipurpose parameter (b>=0, a+b>0)

c

multipurpose parameter

d

multipurpose parameter (d>=1)

teta

position parameter

Details

Probability density function see formula (2.1) in the article Cumulative distribution function see formula (2.2) Quantile functon see formulas (2.3-2.5) Random number generator see proposition (4)

Value

The function returns the value of the quantile function for the Sulewski plasticizing component distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P., Volodin, A. (2022). Sulewski Plasticizing Component Distribution: properties and applications. Lobachtetavskii Journal of Mathtetamatics 43(8), 2286-2300.

Examples

dspc(0,1,1,1,1,0)
pspc(0,1,1,1,1,0)
qspc(0.5,1,1,1,1,0)
rspc(10,1,1,1,1,0)

Two-Piece Power Normal Distribution

Description

Density, distribution function, quantile function and random generation for the two-piece power normal distribution with parameters teta, s1, s2 and c.

Usage

qtppn(p, teta, s1, s2, c)

Arguments

p

probability between 0 and 1

teta

position parameter

s1

positive scale parameter

s2

positive scale parameter

c

shape parameter (c>=1)

Details

Probability density function see formula (4) in the article Cumulative distribution function see formula (5) Quantile functon see formula (10) Random number generator see formula (21)

Value

The function returns the value of the quantile function for the two-piece power normal distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2021). Two-Piece Power Normal Distribution, Communications in Statistics - Theory and Method 50(11), 2619-2639.

Examples

dtppn(2,1,1,1,2)
ptppn(2,1,1,1,2)
qtppn(0.5,1,1,1,2)
rtppn(10,1,1,1,2)

DS Normal Distribution

Description

Density, distribution function, quantile function and random generation for the DS normal distribution with parameters a, b, c and d.

Usage

rdsn(n, a, b, c, teta)

Arguments

n

positive number of observations

a

non-negative multipurpose parameter and a+b>0

b

non-negative multipurpose parameter and a+b>0

c

real multipurpose parameter

teta

real position parameter

Details

Probability density function in Latex see formula (5) in the paper Cumulative distribution function in Latex see formula (6) Quantile function see formulas (8,9,10) Random number generator see Theorem (5)

Value

The function returns random generator values for the DS normal distribution

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski P. (2021). DS Normal Distribution: properties and applications. Lobachevskii Journal of Mathematics 42(12), 2980-2999.

Examples

ddsn(-0.5,2,2,2,0)
pdsn(-0.5,2,2,2,0)
qdsn(0.5,2,2,2,0)
rdsn(10,2,2,2,0)

Easily Changeable Kurtosis Distribution

Description

Density, distribution function, quantile function and random generation for the Easily Changeable Kurtosis Distribution with parameters a and p.

Usage

reck(n, a, p)

Arguments

n

positive number of observations

a

positive scale parameter

p

shape parameter: p>-1

Details

Probability density function see formula (1) or (3) in the article Cumulative distribution function see formula (4) Quantile functon see formula (20) Random number generator see formula (41)

Value

The function returns random generation values for the Easily Changeable Kurtosis Distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2022). Easily Changeable Kurtosis Distribution. Austrian Journal of Statistics 52, 1-24.

Examples

deck(1,2,3)
peck(1,2,3)
qeck(0.5,2,3)
reck(10,2,3)

Expnormal Distribution

Description

Density, distribution function, quantile function and random generation for the Expnormal distribution with parameters a1, b1, a2, b2 and c.

Usage

ren(n, a1, b1, a2, b2, c)

Arguments

n

positive number of observations

a1

position parameter

b1

positive scale parameter

a2

position parameter

b2

positive scale parameter

c

semi-fraction parameter

Details

Probability density function see formula (2.1) in the article Cumulative distribution function see formula (2.3) Quantile functon see proposition (2.2) Random number generator see proposition (2.6)

Value

The function returns random generator values for the Expnormal distribution

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2022). New Members of The Johnson Family of Probability Distributions:Properties and Application, Accepted: February 2022. REVSTAT-Statistical Journal.

Examples

den(1,1,2,2,2,1)
pen(1,1,2,2,2,1)
qen(0.5,1,2,2,2,1)
ren(10,1,2,2,2,1)

Plasticizing Component

Description

Density, distribution function, quantile function and random generation for the plasticizing component with parameters teta, s2 and c.

Usage

rpc(n, teta, s2, c)

Arguments

n

positive number of observations

teta

position parameter

s2

positive scale parameter

c

shape parameter (c>=1)

Details

Probability density function see formula (2) in the article Cumulative distribution function see formula (4) Quantile functon see formula (9) Random number generator see formula (23)

Value

The function returns random generator values for the plasticizing component.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2020). Normal Distribution with Plasticizing Component, Communications in Statistics ? Theory and Method 51(11), 3806-3835.

Examples

dpc(0,1,2,2)
ppc(0,1,2,2)
qpc(0.5,1,2,2)
rpc(10,1,2,2)

Sulewski Plasticizing Component Distribution

Description

Density, distribution function, quantile function and random generation for the Sulewski plasticizing component distribution with parameters a, b, c, d and teta.

Usage

rspc(n, a, b, c, d, teta)

Arguments

n

positive number of observations

a

multipurpose parameter (a>=0)

b

multipurpose parameter (b>=0, a+b>0)

c

multipurpose parameter

d

multipurpose parameter (d>=1)

teta

position parameter

Details

Probability density function see formula (2.1) in the article Cumulative distribution function see formula (2.2) Quantile functon see formulas (2.3-2.5) Random number generator see proposition (4)

Value

The function returns random generator values for the Sulewski plasticizing component distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P., Volodin, A. (2022). Sulewski Plasticizing Component Distribution: properties and applications. Lobachtetavskii Journal of Mathtetamatics 43(8), 2286-2300.

Examples

dspc(0,1,1,1,1,0)
pspc(0,1,1,1,1,0)
qspc(0.5,1,1,1,1,0)
rspc(10,1,1,1,1,0)

Two-Piece Power Normal Distribution

Description

Density, distribution function, quantile function and random generation for the two-piece power normal distribution with parameters teta, s1, s2 and c.

Usage

rtppn(n, teta, s1, s2, c)

Arguments

n

positive number of observations

teta

position parameter

s1

positive scale parameter

s2

positive scale parameter

c

shape parameter (c>=1)

Details

Probability density function see formula (4) in the article Cumulative distribution function see formula (5) Quantile functon see formula (10) Random number generator see formula (21)

Value

The function returns random generator values for the two-piece power normal distribution.

Author(s)

Piotr Sulewski, piotr.sulewski@upsl.edu.pl, Pomeranian UNiwersity in Slupsk.

References

Sulewski, P. (2021). Two-Piece Power Normal Distribution, Communications in Statistics - Theory and Method 50(11), 2619-2639.

Examples

dtppn(2,1,1,1,2)
ptppn(2,1,1,1,2)
qtppn(0.5,1,1,1,2)
rtppn(10,1,1,1,2)

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