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.
Value
dwgd
gives the density, pwgd
gives the distribution
function, qwgd
gives the quantile function and rwgd
generates
random deviates.
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 $$x\in \mathbb {N} =1,2,...~,~\lambda >0~and~0<\alpha <1.$$