Package 'new.dist'

Bimodal Weibull Distribution

Description

Density, distribution function, quantile function and random generation for a Bimodal Weibull distribution with parameters shape and scale.

Usage

dbwd(x, alpha, beta = 1, sigma, log = FALSE)

pbwd(q, alpha, beta = 1, sigma, lower.tail = TRUE, log.p = FALSE)

qbwd(p, alpha, beta = 1, sigma, lower.tail = TRUE)

rbwd(n, alpha, beta = 1, sigma)

Arguments

x, q	vector of quantiles.
alpha	a shape parameter.
beta	a scale parameter.
sigma	a control parameter that controls the uni- or bimodality of the distribution.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

A Bimodal Weibull distribution with shape parameter $\alpha$, scale parameter $\beta$,and the control parameter $\sigma$ that determines the uni- or bimodality of the distribution, has density

$f\left( x\right) =\frac{\alpha }{\beta Z_{\theta }} \left[ 1+\left( 1-\sigma~x\right) ^{2}\right] \left( \frac{x}{\beta } \right) ^{\alpha -1}\exp \left( -\left( \frac{x}{\beta }\right) ^{\alpha } \right),$

where

$Z_{\theta }=2+\sigma ^{2}\beta ^{2}\Gamma \left( 1+\left( 2/\alpha \right)\right) -2\sigma \beta \Gamma \left( 1+\left( 1/\alpha \right) \right)$

and

$x\geq 0,~\alpha ,\beta >0~ and ~\sigma \in\mathbb{R}.$

Value

dbwd gives the density, pbwd gives the distribution function, qbwd gives the quantile function and rbwd generates random deviates.

References

Vila, R. ve Niyazi Çankaya, M., 2022, A bimodal Weibull distribution: properties and inference, Journal of Applied Statistics, 49 (12), 3044-3062.

Examples

library(new.dist)
dbwd(1,alpha=2,beta=3,sigma=4)
pbwd(1,alpha=2,beta=3,sigma=4)
qbwd(.7,alpha=2,beta=3,sigma=4)
rbwd(10,alpha=2,beta=3,sigma=4)

---

Discrete Lindley Distribution

Description

Density, distribution function, quantile function and random generation for the discrete Lindley distribution.

Usage

ddLd1(x, theta, log = FALSE)

pdLd1(q, theta, lower.tail = TRUE, log.p = FALSE)

qdLd1(p, theta, lower.tail = TRUE)

rdLd1(n, theta)

Arguments

x, q	vector of quantiles.
theta	a parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The Discrete Lindley distribution with a parameter $\theta$, has density

$f\left( x\right) =\frac{\lambda ^{x}}{1-\log \lambda } \left( \lambda \log\lambda +\left( 1-\lambda \right) \left( 1-\log \lambda^{x+1}\right)\right),$

where

$x=0,1,...,~\theta >0~and~\lambda =e^{-\theta }.$

Value

ddLd1 gives the density, pdLd1 gives the distribution function, qdLd1 gives the quantile function and rdLd1 generates random deviates.

References

Gómez-Déniz, E. ve Calderín-Ojeda, E., 2011, The discrete Lindley distribution: properties and applications.Journal of statistical computation and simulation, 81 (11), 1405-1416.

Examples

library(new.dist)
ddLd1(1,theta=2)
pdLd1(2,theta=1)
qdLd1(.993,theta=2)
rdLd1(10,theta=1)

---

Discrete Lindley Distribution

Description

Density, distribution function, quantile function and random generation for the discrete Lindley distribution.

Usage

ddLd2(x, theta, log = FALSE)

pdLd2(q, theta, lower.tail = TRUE, log.p = FALSE)

qdLd2(p, theta, lower.tail = TRUE)

rdLd2(n, theta)

Arguments

x, q	vector of quantiles.
theta	a parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

the discrete Lindley distribution with a parameter $\theta$, has density

$f\left( x\right) =\frac{\lambda ^{x}}{1+\theta } \left( \theta \left(1-2\lambda \right) +\left( 1-\lambda \right) \left( 1+\theta x\right)\right),$

where

$x=0,1,2,...~,\lambda =\exp \left( -\theta \right) ~and~\theta >0.$

Value

ddLd2 gives the density, pdLd2 gives the distribution function, qdLd2 gives the quantile function and rdLd2 generates random deviates.

References

Bakouch, H. S., Jazi, M. A. ve Nadarajah, S., 2014, A new discrete distribution, Statistics, 48 (1), 200-240.

Examples

library(new.dist)
ddLd2(2,theta=2)
pdLd2(1,theta=2)
qdLd2(.5,theta=2)
rdLd2(10,theta=1)

---

EP distribution

Description

Density, distribution function, quantile function and random generation for the EP distribution.

Usage

dEPd(x, lambda, beta, log = FALSE)

pEPd(q, lambda, beta, lower.tail = TRUE, log.p = FALSE)

qEPd(p, lambda, beta, lower.tail = TRUE)

rEPd(n, lambda, beta)

Arguments

x, q	vector of quantiles.
lambda, beta	are parameters.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The EP distribution with parameters $\lambda$ and $\beta$, has density

$f\left( x\right) =\frac{\lambda \beta } {\left( 1-e^{-\lambda }\right) } e^{-\lambda -\beta x+\lambda e^{-\beta x}},$

where

$x>\mathbb{R}_{+},~\beta ,\lambda \in \mathbb{R}_{+}.$

Value

dEPd gives the density, pEPd gives the distribution function, qEPd gives the quantile function and rEPd generates random deviates.

References

Kuş, C., 2007, A new lifetime distribution, Computational Statistics & Data Analysis, 51 (9), 4497-4509.

Examples

library(new.dist)
dEPd(1, lambda=2, beta=3)
pEPd(1,lambda=2,beta=3)
qEPd(.8,lambda=2,beta=3)
rEPd(10,lambda=2,beta=3)

---

Gamma-Lomax Distribution

Description

Density, distribution function, quantile function and random generation for the gamma-Lomax distribution with parameters shapes and scale.

Usage

dgld(x, a, alpha, beta = 1, log = FALSE)

pgld(q, a, alpha, beta = 1, lower.tail = TRUE, log.p = FALSE)

qgld(p, a, alpha, beta = 1, lower.tail = TRUE)

rgld(n, a, alpha, beta = 1)

Arguments

x, q	vector of quantiles.
a, alpha	are shape parameters.
beta	a scale parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The Gamma-Lomax distribution shape parameters $a$ and $\alpha$, and scale parameter is $\beta$, has density

$f\left( x\right) =\frac{\alpha \beta ^{\alpha }} {\Gamma \left( a\right)\left( \beta +x\right) ^{\alpha +1}}\left\{ -\alpha \log \left( \frac{\beta }{\beta +x}\right) \right\} ^{a-1},$

where

$x>0,~a,\alpha ,\beta >0.$

Value

dgld gives the density, pgld gives the distribution function, qgld gives the quantile function and rgld generates random deviates.

References

Cordeiro, G. M., Ortega, E. M. ve Popović, B. V., 2015, The gamma-Lomax distribution, Journal of statistical computation and simulation, 85 (2), 305-319.

Ristić, M. M., & Balakrishnan, N. (2012), The gamma-exponentiated exponential distribution. Journal of statistical computation and simulation , 82(8), 1191-1206.

Examples

library(new.dist)
dgld(1, a=2, alpha=3, beta=4)
pgld(1, a=2,alpha=3,beta=4)
qgld(.8, a=2,alpha=3,beta=4)
rgld(10, a=2,alpha=3,beta=4)

---

Kumaraswamy Distribution

Description

Density, distribution function, quantile function and random generation for Kumaraswamy distribution with shape parameters.

Usage

dkd(x, lambda, alpha, log = FALSE)

pkd(q, lambda, alpha, lower.tail = TRUE, log.p = FALSE)

qkd(p, lambda, alpha, lower.tail = TRUE)

rkd(n, lambda, alpha)

Arguments

x, q	vector of quantiles.
alpha, lambda	are non-negative shape parameters.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

Kumaraswamy distribution with non-negative shape parameters $\alpha$ and $\lambda$ has density

$f\left( x\right) =\alpha \lambda x^{\lambda -1}\left( 1-x^{\lambda } \right)^{\alpha -1},$

where

$0<x<1,~~\alpha ,\lambda >0.$

Value

dkd gives the density, pkd gives the distribution function, qkd gives the quantile function and rkd generates random deviates.

References

Kohansal, A. ve Bakouch, H. S., 2021, Estimation procedures for Kumaraswamy distribution parameters under adaptive type-II hybrid progressive censoring, Communications in Statistics-Simulation and Computation, 50 (12), 4059-4078.

Examples

library("new.dist")
dkd(0.1,lambda=2,alpha=3)
pkd(0.5,lambda=2,alpha=3)
qkd(.8,lambda=2,alpha=3)
rkd(10,lambda=2,alpha=3)

---

Lindley Distribution

Description

Density, distribution function, quantile function and random generation for the Lindley distribution.

Usage

dLd(x, theta, log = FALSE)

pLd(q, theta, lower.tail = TRUE, log.p = FALSE)

qLd(p, theta, lower.tail = TRUE)

rLd(n, theta)

Arguments

x, q	vector of quantiles.
theta	a parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The Lindley distribution with a parameter $\theta$, has density

$f\left( x\right) =\frac{\theta ^{2}}{1+\theta }\left( 1+x\right) e^{-\theta~x},$

where

$x>0,~\theta >0.$

Value

dLd gives the density, pLd gives the distribution function, qLd gives the quantile function and rLd generates random deviates.

References

Akgül, F. G., Acıtaş, Ş. ve Şenoğlu, B., 2018, Inferences on stress–strength reliability based on ranked set sampling data in case of Lindley distribution, Journal of statistical computation and simulation, 88 (15), 3018-3032.

Examples

library(new.dist)
dLd(1,theta=2)
pLd(1,theta=2)
qLd(.8,theta=1)
rLd(10,theta=1)

---

Maxwell Distribution

Description

Density, distribution function, quantile function and random generation for Maxwell distribution with parameter scale.

Usage

dmd(x, theta = 1, log = FALSE)

pmd(q, theta = 1, lower.tail = TRUE, log.p = FALSE)

qmd(p, theta = 1, lower.tail = TRUE)

rmd(n, theta = 1)

Arguments

x, q	vector of quantiles.
theta	a scale parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

Maxwell distribution with scale parameter $\theta$, has density

$f\left( x\right) =\frac{4}{\sqrt{\pi }} \frac{1}{\theta ^{3/2}}x^{2}e^{-x^{2}/\theta },$

where

$0\leq x<\infty ,~~\theta >0.$

Value

dmd gives the density, pmd gives the distribution function, qmd gives the quantile function and rmd generates random deviates.

References

Krishna, H., Vivekanand ve Kumar, K., 2015, Estimation in Maxwell distribution with randomly censored data, Journal of statistical computation and simulation, 85 (17), 3560-3578.

Examples

library(new.dist)
dmd(1,theta=2)
pmd(1,theta=2)
qmd(.4,theta=5)
rmd(10,theta=1)

---

Muth Distribution

Description

Density, distribution function, quantile function and random generation for on the Muth distribution.

Usage

domd(x, alpha, log = FALSE)

pomd(q, alpha, lower.tail = TRUE, log.p = FALSE)

qomd(p, alpha, lower.tail = TRUE)

romd(n, alpha)

Arguments

x, q	vector of quantiles.
alpha	a parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The Muth distribution with a parameter $\alpha$, has density

$f\left( x\right) =\left( e^{\alpha x}- \alpha \right) e^{\alpha x-\left(1/\alpha \right) \left( e^{\alpha x}- 1\right) },$

where

$x>0,~\alpha \in \left( 0,1\right].$

Value

domd gives the density, pomd gives the distribution function, qomd gives the quantile function and romd generates random deviates.

References

Jodrá, P., Jiménez-Gamero, M. D. ve Alba-Fernández, M. V., 2015, On the Muth distribution, Mathematical Modelling and Analysis, 20 (3), 291-310.

Examples

library(new.dist)
domd(1,alpha=.2)
pomd(1,alpha=.2)
qomd(.8,alpha=.1)
romd(10,alpha=1)

---

Power Log Dagum Distribution

Description

Density, distribution function, quantile function and random generation for a Power Log Dagum distribution.

Usage

dpldd(x, alpha, beta, theta, log = FALSE)

ppldd(q, alpha, beta, theta, lower.tail = TRUE, log.p = FALSE)

qpldd(p, alpha, beta, theta, lower.tail = TRUE)

rpldd(n, alpha, beta, theta)

Arguments

x, q	vector of quantiles.
alpha, beta, theta	are parameters.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

A Power Log Dagum Distribution with parameters $\alpha$, $\beta$ and $\theta$, has density

$f\left( x\right) =\alpha \left( \beta +\theta \left\vert x\right\vert^{\beta -1} \right) e^{-\left( \beta x+sign\left( x\right) \left( \theta/\beta \right) \left\vert x\right\vert ^{\beta }\right) ~}~\left(1+e^{-\left( \beta x+sign \left( x\right)\left( \theta /\beta \right) \left\vert x\right\vert ^{\beta }\right) } \right) ^{-\left( \alpha +1\right)},$

where

$x\in \mathbb{R},~\beta \in \mathbb{R},~\alpha >0~and~\theta \geq 0$

Value

dpldd gives the density, ppldd gives the distribution function, qpldd gives the quantile function and rpldd generates random deviates.

Note

The distributions hazard function

$h\left( x\right) =\frac{\alpha \left( \beta +\theta \left\vert x\right\vert^{\beta -1} \right) e^{-\left( \beta x+sign\left( x\right) \left( \theta/\beta \right) \left\vert x\right\vert ^{\beta }\right) }\left( 1+e^{-\left(\beta x+sign \left( x\right) \left( \theta /\beta \right) \left\vert x \right\vert ^{\beta }\right) }\right) ^{-\left(\alpha +1\right) }} {1-\left( 1+e^{-\left( \beta x+sign\left( x\right) \left( \theta / \beta \right) \left\vert x\right\vert ^{\beta }\right) } \right) ^{-\alpha }} .$

References

Bakouch, H. S., Khan, M. N., Hussain, T. ve Chesneau, C., 2019, A power log-Dagum distribution: estimation and applications, Journal of Applied Statistics, 46 (5), 874-892.

Examples

library(new.dist)
dpldd(1, alpha=2, beta=3, theta=4)
ppldd(1,alpha=2,beta=3,theta=4)
qpldd(.8,alpha=2,beta=3,theta=4)
rpldd(10,alpha=2,beta=3,theta=4)

---

Ram Awadh Distribution

Description

Density, distribution function, quantile function and random generation for a Ram Awadh distribution with parameter scale.

Usage

dRA(x, theta = 1, log = FALSE)

pRA(q, theta = 1, lower.tail = TRUE, log.p = FALSE)

qRA(p, theta = 1, lower.tail = TRUE)

rRA(n, theta = 1)

Arguments

x, q	vector of quantiles.
theta	a scale parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

Ram Awadh distribution with scale parameter $\theta$, has density

$f\left( x\right) =\frac{\theta ^{6}}{\theta ^{6}+120} \left( \theta+x^{5}\right) e^{-\theta x},$

where

$x>0,~\theta >0.$

Value

dRA gives the density, pRA gives the distribution function, qRA gives the quantile function and rRA generates random deviates.

References

Shukla, K. K., Shanker, R. ve Tiwari, M. K., 2022, A new one parameter discrete distribution and its applications, Journal of Statistics and Management Systems, 25 (1), 269-283.

Examples

library(new.dist)
dRA(1,theta=2)
pRA(1,theta=2)
qRA(.1,theta=1)
rRA(10,theta=1)

---

Slashed Generalized Rayleigh Distribution

Description

Density, distribution function, quantile function and random generation for the Slashed generalized Rayleigh distribution with parameters shape, scale and kurtosis.

Usage

dsgrd(x, theta, alpha, beta, log = FALSE)

psgrd(q, theta, alpha, beta, lower.tail = TRUE, log.p = FALSE)

qsgrd(p, theta, alpha, beta, lower.tail = TRUE)

rsgrd(n, theta, alpha, beta)

Arguments

x, q	vector of quantiles.
theta	a scale parameter.
alpha	a shape parameter.
beta	a kurtosis parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The Slashed Generalized Rayleigh distribution with shape parameter $\alpha$, scale parameter $\theta$ and kurtosis parameter $\beta$, has density

$f\left( x\right) =\frac{\beta x^{-\left( \beta+1\right)}}{\Gamma \left( \alpha+1\right) \theta ^{\beta/2}}\Gamma \left( \frac{2\alpha +\beta +2}{2} \right)F\left( \theta x^{2};\frac{2\alpha +\beta +2}{2},1\right),$

where F(.;a,b) is the cdf of the Gamma (a,b) distribution, and

$x>0,~\theta >0,~\alpha >-1~and~\beta >0$

Value

dsgrd gives the density, psgrd gives the distribution function, qsgrd gives the quantile function and rsgrd generates random deviates.

References

Iriarte, Y. A., Vilca, F., Varela, H. ve Gómez, H. W., 2017, Slashed generalized Rayleigh distribution, Communications in Statistics- Theory and Methods, 46 (10), 4686-4699.

Examples

library(new.dist)
dsgrd(2,theta=3,alpha=1,beta=4)
psgrd(5,theta=3,alpha=1,beta=4)
qsgrd(.4,theta=3,alpha=1,beta=4)
rsgrd(10,theta=3,alpha=1,beta=4)

---

Standard Omega Distribution

Description

Density, distribution function, quantile function and random generation for the Standard Omega distribution.

Usage

dsod(x, alpha, beta, log = FALSE)

psod(q, alpha, beta, lower.tail = TRUE, log.p = FALSE)

qsod(p, alpha, beta, lower.tail = TRUE)

rsod(n, alpha, beta)

Arguments

x, q	vector of quantiles.
alpha, beta	are parameters.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The Standard Omega distribution with parameters $\alpha$ and $\beta$, has density

$f\left( x\right) =\alpha \beta x^{\beta -1}\frac{1}{1-x^{2\beta }} \left( \frac{1+x^{\beta }}{1-x^{\beta }}\right) ^{-\alpha /2},$

where

$0<x<1,~\alpha ,\beta >0.$

Value

dsod gives the density, psod gives the distribution function, qsod gives the quantile function and rsod generates random deviates.

References

Birbiçer, İ. ve Genç, A. İ., 2022, On parameter estimation of the standard omega distribution. Journal of Applied Statistics, 1-17.

Examples

library(new.dist)
dsod(0.4, alpha=1, beta=2)
psod(0.4, alpha=1, beta=2)
qsod(.8, alpha=1, beta=2)
rsod(10, alpha=1, beta=2)

---

Power Muth Distribution

Description

Density, distribution function, quantile function and random generation for the Power Muth distribution with parameters shape and scale.

Usage

dtpmd(x, beta = 1, alpha, log = FALSE)

ptpmd(q, beta = 1, alpha, lower.tail = TRUE, log.p = FALSE)

qtpmd(p, beta = 1, alpha, lower.tail = TRUE)

rtpmd(n, beta = 1, alpha)

Arguments

x, q	vector of quantiles.
beta	a scale parameter.
alpha	a shape parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The Power Muth distribution with shape parameter $\alpha$ and scale parameter $\beta$ has density

$f\left( x\right) =\frac{\alpha }{\beta ^\alpha }x^{\alpha -1} \left( e^{\left(x/\beta \right) ^{\alpha }}-1\right) \left( e^{\left( x/\beta \right) ^{\alpha }- \left( e^{\left( x/\beta \right) ^{\alpha }}-1\right) }\right),$

where

$x>0,~\alpha ,\beta>0.$

Value

dtpmd gives the density, ptpmd gives the distribution function, qtpmd gives the quantile function and rtpmd generates random deviates.

Note

Hazard function;

$h\left( \beta ,\alpha \right) =\frac{\alpha }{\beta ^{\alpha }} \left(e^{\left( x/\beta \right) ^{\alpha }}-1\right) x^{\alpha -1}$

References

Jodra, P., Gomez, H. W., Jimenez-Gamero, M. D., & Alba-Fernandez, M. V. (2017). The power Muth distribution . Mathematical Modelling and Analysis, 22(2), 186-201.

Examples

library(new.dist)
dtpmd(1, beta=2, alpha=3)
ptpmd(1,beta=2,alpha=3)
qtpmd(.5,beta=2,alpha=3)
rtpmd(10,beta=2,alpha=3)

---

Two-Parameter Rayleigh Distribution

Description

Density, distribution function, quantile function and random generation for the Two-Parameter Rayleigh distribution with parameters location and scale.

Usage

dtprd(x, lambda = 1, mu, log = FALSE)

ptprd(q, lambda = 1, mu, lower.tail = TRUE, log.p = FALSE)

qtprd(p, lambda = 1, mu, lower.tail = TRUE)

rtprd(n, lambda = 1, mu)

Arguments

x, q	vector of quantiles.
lambda	a scale parameter.
mu	a location parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The Two-Parameter Rayleigh distribution with scale parameter $\lambda$ and location parameter $\mu$, has density

$f\left( x\right) =2\lambda \left( x-\mu \right) e^{-\lambda \left( x-\mu\right) ^{2}},$

where

$x>\mu ,~\lambda >0.$

Value

dtprd gives the density, ptprd gives the distribution function, qtprd gives the quantile function and rtprd generates random deviates.

References

Dey, S., Dey, T. ve Kundu, D., 2014, Two-parameter Rayleigh distribution: different methods of estimation, American Journal of Mathematical and Management Sciences, 33 (1), 55-74.

Examples

library(new.dist)
dtprd(5, lambda=4, mu=4)
ptprd(2,lambda=2,mu=1)
qtprd(.5,lambda=2,mu=1)
rtprd(10,lambda=2,mu=1)

---

Uniform-Geometric Distribution

Description

Density, distribution function, quantile function and random generation for the Uniform-Geometric distribution.

Usage

dugd(x, theta, log = FALSE)

pugd(q, theta, lower.tail = TRUE, log.p = FALSE)

qugd(p, theta, lower.tail = TRUE)

rugd(n, theta)

Arguments

x, q	vector of quantiles.
theta	a parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The Uniform-Geometric distribution with shape parameter $\theta$, has density

$f\left( x\right) =\theta \left( 1-\theta \right) ^{x-1}LerchPhi \left[ \left(1-\theta \right) ,1,x\right],$

where

$LerchPhi\left( z,a,v\right) =\sum_{n=0}^{\infty }\frac{z^{n}} {\left(v+n\right) ^{a}}$

and

$x=1,2,...~,~~0<\theta <1.$

Value

dugd gives the density, pugd gives the distribution function, qugd gives the quantile function and rugd generates random deviates.

References

Akdoğan, Y., Kuş, C., Asgharzadeh, A., Kınacı, İ., & Sharafi, F. (2016). Uniform-geometric distribution. Journal of Statistical Computation and Simulation, 86(9), 1754-1770.

Examples

library(new.dist)
dugd(1, theta=0.5)
pugd(1,theta=.5)
qugd(0.6,theta=.1)
rugd(10,theta=.1)

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Unit Inverse Gaussian Distribution

Description

Density, distribution function, quantile function and random generation for the Unit Inverse Gaussian distribution mean and scale.

Usage

duigd(x, mu, lambda = 1, log = FALSE)

puigd(q, mu, lambda = 1, lower.tail = TRUE, log.p = FALSE)

quigd(p, mu, lambda = 1, lower.tail = TRUE)

ruigd(n, mu, lambda = 1)

Arguments

x, q	vector of quantiles.
mu	a mean parameter.
lambda	a scale parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The Unit Inverse Gaussian distribution scale parameter $\lambda$ and mean parameter $\mu$, has density

$f\left( x\right) =\sqrt{\frac{\lambda }{2\pi }} \frac{1}{x^{3/2}}e^{-\frac{ \lambda }{2\mu ^{2}x}\left( x-\mu \right) ^{2}},$

where

$x>0,~\mu ,\lambda >0.$

Value

duigd gives the density, puigd gives the distribution function, quigd gives the quantile function and ruigd generates random deviates.

References

Ghitany, M., Mazucheli, J., Menezes, A. ve Alqallaf, F., 2019, The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval, Communications in Statistics-Theory and Methods, 48 (14), 3423-3438.

Examples

library(new.dist)
duigd(1, mu=2, lambda=3)
puigd(1,mu=2,lambda=3)
quigd(.1,mu=2,lambda=3)
ruigd(10,mu=2,lambda=3)

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Weighted Geometric Distribution

Description

Density, distribution function, quantile function and random generation for the Weighted Geometric distribution.

Usage

dwgd(x, alpha, lambda, log = FALSE)

pwgd(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)

qwgd(p, alpha, lambda, lower.tail = TRUE)

rwgd(n, alpha, lambda)

Arguments

x, q	vector of quantiles.
alpha, lambda	are parameters.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P\left[ X\leq x\right]$, otherwise, $P\left[ X>x\right]$.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The Weighted Geometric distribution with parameters $\alpha$ and $\lambda$, has density

$f\left( x\right) =\frac{\left( 1-\alpha \right) \left( 1-\alpha ^{\lambda+1}\right) }{1-\alpha ^{\lambda }}\alpha ^{x-1} \left( 1-\alpha ^{\lambda x}\right),$

where

$x\in \mathbb {N} =1,2,...~,~\lambda >0~and~0<\alpha <1.$

Value

dwgd gives the density, pwgd gives the distribution function, qwgd gives the quantile function and rwgd generates random deviates.

References

Najarzadegan, H., Alamatsaz, M. H., Kazemi, I. ve Kundu, D., 2020, Weighted bivariate geometric distribution: Simulation and estimation, Communications in Statistics-Simulation and Computation, 49 (9), 2419-2443.

Examples

library(new.dist)
dwgd(1,alpha=.2,lambda=3)
pwgd(1,alpha=.2,lambda=3)
qwgd(.98,alpha=.2,lambda=3)
rwgd(10,alpha=.2,lambda=3)

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