new.dist (version 0.1.1)

gld: 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)

Value

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

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

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)