wgd {new.dist}

Weighted Geometric Distribution

Description

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.

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.

Value

dwgd gives the density, pwgd gives the distribution function, qwgd gives the quantile function and rwgd generates random deviates.

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.

Examples

library(new.dist)
dwgd(1,alpha=.2,lambda=3)
pwgd(1,alpha=.2,lambda=3)
qwgd(.98,alpha=.2,lambda=3)
rwgd(10,alpha=.2,lambda=3)