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