gld {new.dist}

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)