| Title: | Distributions Derived from Normal Distribution |
|---|---|
| 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>. |
| Authors: | Piotr Sulewski [aut, cre]
|
| Maintainer: | Piotr Sulewski <[email protected]> |
| License: | GPL-3 |
| Version: | 0.0.1 |
| Built: | 2024-12-25 06:32:02 UTC |
| Source: | CRAN |
Density, distribution function, quantile function and random generation for the DS normal distribution with parameters a, b, c and d.
ddsn(x, a, b, c, teta)ddsn(x, a, b, c, teta)
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 |
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)
The function returns the value of the probability density function for the DS normal distribution
Piotr Sulewski, [email protected], Pomeranian Uniwersity in Slupsk.
Sulewski P. (2021). DS Normal Distribution: properties and applications. Lobachevskii Journal of Mathematics 42(12), 2980-2999.
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)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)
Density, distribution function, quantile function and random generation for the Easily Changeable Kurtosis Distribution with parameters a and p.
deck(x, a, p)deck(x, a, p)
x |
-a<x<a for -1<p<0 or -a<=x<=a for p>=1 |
a |
positive scale parameter |
p |
shape parameter: p>-1 |
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)
The function returns the value of the probability density function for the Easily Changeable Kurtosis Distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2022). Easily Changeable Kurtosis Distribution. Austrian Journal of Statistics 52, 1-24.
deck(1,2,3) peck(1,2,3) qeck(0.5,2,3) reck(10,2,3)deck(1,2,3) peck(1,2,3) qeck(0.5,2,3) reck(10,2,3)
Density, distribution function, quantile function and random generation for the Expnormal distribution with parameters a1, b1, a2, b2 and c.
den(x, a1, b1, a2, b2, c)den(x, a1, b1, a2, b2, c)
x |
real argument |
a1 |
position parameter |
b1 |
positive scale parameter |
a2 |
position parameter |
b2 |
positive scale parameter |
c |
semi-fraction parameter |
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)
The function returns the value of the probability density function for the Expnormal distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2022). New Members of The Johnson Family of Probability Distributions:Properties and Application, Accepted: February 2022. REVSTAT-Statistical Journal.
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)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)
Density, distribution function, quantile function and random generation for the plasticizing component with parameters teta, s2 and c.
dpc(x, teta, s2, c)dpc(x, teta, s2, c)
x |
real argument |
teta |
position parameter |
s2 |
positive scale parameter |
c |
shape parameter (c>=1) |
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)
The function returns the value of the probability density function for the plasticizing component.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2020). Normal Distribution with Plasticizing Component, Communications in Statistics ? Theory and Method 51(11), 3806-3835.
dpc(0,1,2,2) ppc(0,1,2,2) qpc(0.5,1,2,2) rpc(10,1,2,2)dpc(0,1,2,2) ppc(0,1,2,2) qpc(0.5,1,2,2) rpc(10,1,2,2)
Density, distribution function, quantile function and random generation for the Sulewski plasticizing component distribution with parameters a, b, c, d and teta.
dspc(x, a, b, c, d, teta)dspc(x, a, b, c, d, teta)
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 |
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)
The function returns the value of the probability density function for the Sulewski plasticizing component distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P., Volodin, A. (2022). Sulewski Plasticizing Component Distribution: properties and applications. Lobachtetavskii Journal of Mathtetamatics 43(8), 2286-2300.
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)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)
Density, distribution function, quantile function and random generation for the two-piece power normal distribution with parameters teta, s1, s2 and c.
dtppn(x, teta, s1, s2, c)dtppn(x, teta, s1, s2, c)
x |
real argument |
teta |
position parameter |
s1 |
positive scale parameter |
s2 |
positive scale parameter |
c |
shape parameter (c>=1) |
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)
The function returns the value of the probability density function for the two-piece power normal distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2021). Two-Piece Power Normal Distribution, Communications in Statistics - Theory and Method 50(11), 2619-2639.
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)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)
Density, distribution function, quantile function and random generation for the DS normal distribution with parameters a, b, c and d.
pdsn(x, a, b, c, teta)pdsn(x, a, b, c, teta)
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 |
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)
The function returns the value of the cumulative distribution function for the DS normal distribution
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski P. (2021). DS Normal Distribution: properties and applications. Lobachevskii Journal of Mathematics 42(12), 2980-2999.
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)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)
Density, distribution function, quantile function and random generation for the Easily Changeable Kurtosis Distribution with parameters a and p.
peck(x, a, p)peck(x, a, p)
x |
-a<x<a for -1<p<0 or -a<=x<=a for p>=1 |
a |
positive scale parameter |
p |
shape parameter: p>-1 |
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)
The function returns the value of the cumulative distribution function for the Easily Changeable Kurtosis Distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2022). Easily Changeable Kurtosis Distribution. Austrian Journal of Statistics 52, 1-24.
deck(1,2,3) peck(1,2,3) qeck(0.5,2,3) reck(10,2,3)deck(1,2,3) peck(1,2,3) qeck(0.5,2,3) reck(10,2,3)
Density, distribution function, quantile function and random generation for the Expnormal distribution with parameters a1, b1, a2, b2 and c.
pen(x, a1, b1, a2, b2, c)pen(x, a1, b1, a2, b2, c)
x |
real argument |
a1 |
position parameter |
b1 |
positive scale parameter |
a2 |
position parameter |
b2 |
positive scale parameter |
c |
semi-fraction parameter |
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)
The function returns the value of the cumulative distribution function for the Expnormal distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2022). New Members of The Johnson Family of Probability Distributions:Properties and Application, Accepted: February 2022. REVSTAT-Statistical Journal.
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)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)
Density, distribution function, quantile function and random generation for the plasticizing component with parameters teta, s2 and c.
ppc(x, teta, s2, c)ppc(x, teta, s2, c)
x |
real argument |
teta |
position parameter |
s2 |
positive scale parameter |
c |
shape parameter (c>=1) |
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)
The function returns the value of the cumulative distribution function for the plasticizing component.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2020). Normal Distribution with Plasticizing Component, Communications in Statistics ? Theory and Method 51(11), 3806-3835.
dpc(0,1,2,2) ppc(0,1,2,2) qpc(0.5,1,2,2) rpc(10,1,2,2)dpc(0,1,2,2) ppc(0,1,2,2) qpc(0.5,1,2,2) rpc(10,1,2,2)
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:
#' @section Functions for the expnormal distribution:
#' @section Functions for the Sulewski plasticizing component distribution:
#' @section Functions for the easily changeable kurtosis distribution:
Density, distribution function, quantile function and random generation for the Sulewski plasticizing component distribution with parameters a, b, c, d and teta.
pspc(x, a, b, c, d, teta)pspc(x, a, b, c, d, teta)
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 |
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)
The function returns the value of the cumulative distribution function for the Sulewski plasticizing component distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P., Volodin, A. (2022). Sulewski Plasticizing Component Distribution: properties and applications. Lobachtetavskii Journal of Mathtetamatics 43(8), 2286-2300.
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)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)
Density, distribution function, quantile function and random generation for the two-piece power normal distribution with parameters teta, s1, s2 and c.
ptppn(x, teta, s1, s2, c)ptppn(x, teta, s1, s2, c)
x |
real argument |
teta |
position parameter |
s1 |
positive scale parameter |
s2 |
positive scale parameter |
c |
shape parameter (c>=1) |
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)
The function returns the value of the cumulative distribution function for the two-piece power normal distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2021). Two-Piece Power Normal Distribution, Communications in Statistics - Theory and Method 50(11), 2619-2639.
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)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)
Density, distribution function, quantile function and random generation for the DS normal distribution with parameters a, b, c and d.
qdsn(p, a, b, c, teta)qdsn(p, a, b, c, teta)
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 |
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)
The function returns the value of the quantile function for the DS normal distribution
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski P. (2021). DS Normal Distribution: properties and applications. Lobachevskii Journal of Mathematics 42(12), 2980-2999.
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)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)
Density, distribution function, quantile function and random generation for the Easily Changeable Kurtosis Distribution with parameters a and p.
qeck(q, a, p)qeck(q, a, p)
q |
probability between 0 and 1 |
a |
positive scale parameter |
p |
shape parameter: p>-1 |
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)
The function returns the value of the quantile function for the Easily Changeable Kurtosis Distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2022). Easily Changeable Kurtosis Distribution. Austrian Journal of Statistics 52, 1-24.
deck(1,2,3) peck(1,2,3) qeck(0.5,2,3) reck(10,2,3)deck(1,2,3) peck(1,2,3) qeck(0.5,2,3) reck(10,2,3)
Density, distribution function, quantile function and random generation for the Expnormal distribution with parameters a1, b1, a2, b2 and c.
qen(p, a1, b1, a2, b2, c)qen(p, a1, b1, a2, b2, c)
p |
probability between 0 and 1 |
a1 |
position parameter |
b1 |
positive scale parameter |
a2 |
position parameter |
b2 |
positive scale parameter |
c |
semi-fraction parameter |
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)
The function returns the value of the quantile function for the Expnormal distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2022). New Members of The Johnson Family of Probability Distributions:Properties and Application, Accepted: February 2022. REVSTAT-Statistical Journal.
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)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)
Density, distribution function, quantile function and random generation for the plasticizing component with parameters teta, s2 and c.
qpc(p, teta, s2, c)qpc(p, teta, s2, c)
p |
probability between 0 and 1 |
teta |
position parameter |
s2 |
positive scale parameter |
c |
shape parameter (c>=1) |
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)
The function returns the value of the quantile function for the plasticizing component.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
SSulewski, P. (2020). Normal Distribution with Plasticizing Component, Communications in Statistics ? Theory and Method 51(11), 3806-3835.
dpc(0,1,2,2) ppc(0,1,2,2) qpc(0.5,1,2,2) rpc(10,1,2,2)dpc(0,1,2,2) ppc(0,1,2,2) qpc(0.5,1,2,2) rpc(10,1,2,2)
Density, distribution function, quantile function and random generation for the Sulewski plasticizing component distribution with parameters a, b, c, d and teta.
qspc(p, a, b, c, d, teta)qspc(p, a, b, c, d, teta)
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 |
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)
The function returns the value of the quantile function for the Sulewski plasticizing component distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P., Volodin, A. (2022). Sulewski Plasticizing Component Distribution: properties and applications. Lobachtetavskii Journal of Mathtetamatics 43(8), 2286-2300.
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)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)
Density, distribution function, quantile function and random generation for the two-piece power normal distribution with parameters teta, s1, s2 and c.
qtppn(p, teta, s1, s2, c)qtppn(p, teta, s1, s2, c)
p |
probability between 0 and 1 |
teta |
position parameter |
s1 |
positive scale parameter |
s2 |
positive scale parameter |
c |
shape parameter (c>=1) |
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)
The function returns the value of the quantile function for the two-piece power normal distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2021). Two-Piece Power Normal Distribution, Communications in Statistics - Theory and Method 50(11), 2619-2639.
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)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)
Density, distribution function, quantile function and random generation for the DS normal distribution with parameters a, b, c and d.
rdsn(n, a, b, c, teta)rdsn(n, a, b, c, teta)
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 |
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)
The function returns random generator values for the DS normal distribution
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski P. (2021). DS Normal Distribution: properties and applications. Lobachevskii Journal of Mathematics 42(12), 2980-2999.
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)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)
Density, distribution function, quantile function and random generation for the Easily Changeable Kurtosis Distribution with parameters a and p.
reck(n, a, p)reck(n, a, p)
n |
positive number of observations |
a |
positive scale parameter |
p |
shape parameter: p>-1 |
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)
The function returns random generation values for the Easily Changeable Kurtosis Distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2022). Easily Changeable Kurtosis Distribution. Austrian Journal of Statistics 52, 1-24.
deck(1,2,3) peck(1,2,3) qeck(0.5,2,3) reck(10,2,3)deck(1,2,3) peck(1,2,3) qeck(0.5,2,3) reck(10,2,3)
Density, distribution function, quantile function and random generation for the Expnormal distribution with parameters a1, b1, a2, b2 and c.
ren(n, a1, b1, a2, b2, c)ren(n, a1, b1, a2, b2, c)
n |
positive number of observations |
a1 |
position parameter |
b1 |
positive scale parameter |
a2 |
position parameter |
b2 |
positive scale parameter |
c |
semi-fraction parameter |
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)
The function returns random generator values for the Expnormal distribution
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2022). New Members of The Johnson Family of Probability Distributions:Properties and Application, Accepted: February 2022. REVSTAT-Statistical Journal.
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)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)
Density, distribution function, quantile function and random generation for the plasticizing component with parameters teta, s2 and c.
rpc(n, teta, s2, c)rpc(n, teta, s2, c)
n |
positive number of observations |
teta |
position parameter |
s2 |
positive scale parameter |
c |
shape parameter (c>=1) |
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)
The function returns random generator values for the plasticizing component.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2020). Normal Distribution with Plasticizing Component, Communications in Statistics ? Theory and Method 51(11), 3806-3835.
dpc(0,1,2,2) ppc(0,1,2,2) qpc(0.5,1,2,2) rpc(10,1,2,2)dpc(0,1,2,2) ppc(0,1,2,2) qpc(0.5,1,2,2) rpc(10,1,2,2)
Density, distribution function, quantile function and random generation for the Sulewski plasticizing component distribution with parameters a, b, c, d and teta.
rspc(n, a, b, c, d, teta)rspc(n, a, b, c, d, teta)
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 |
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)
The function returns random generator values for the Sulewski plasticizing component distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P., Volodin, A. (2022). Sulewski Plasticizing Component Distribution: properties and applications. Lobachtetavskii Journal of Mathtetamatics 43(8), 2286-2300.
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)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)
Density, distribution function, quantile function and random generation for the two-piece power normal distribution with parameters teta, s1, s2 and c.
rtppn(n, teta, s1, s2, c)rtppn(n, teta, s1, s2, c)
n |
positive number of observations |
teta |
position parameter |
s1 |
positive scale parameter |
s2 |
positive scale parameter |
c |
shape parameter (c>=1) |
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)
The function returns random generator values for the two-piece power normal distribution.
Piotr Sulewski, [email protected], Pomeranian UNiwersity in Slupsk.
Sulewski, P. (2021). Two-Piece Power Normal Distribution, Communications in Statistics - Theory and Method 50(11), 2619-2639.
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)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)