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