Density, distribution function, quantile function and random generation for
the Uniform-Geometric distribution.
Usage
dugd(x, theta, log = FALSE)
pugd(q, theta, lower.tail = TRUE, log.p = FALSE)
qugd(p, theta, lower.tail = TRUE)
rugd(n, theta)
Value
dugd gives the density, pugd gives the distribution
function, qugd gives the quantile function and rugd generates
random deviates.
Arguments
x, q
vector of quantiles.
theta
a 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 Uniform-Geometric distribution with shape parameter \(\theta\), has
density
$$f\left( x\right) =\theta \left( 1-\theta \right) ^{x-1}LerchPhi
\left[ \left(1-\theta \right) ,1,x\right],$$
where
$$LerchPhi\left( z,a,v\right) =\sum_{n=0}^{\infty }\frac{z^{n}}
{\left(v+n\right) ^{a}}$$
and
$$x=1,2,...~,~~0<\theta <1.$$
References
Akdoğan, Y., Kuş, C., Asgharzadeh, A., Kınacı, İ., & Sharafi,
F. (2016).
Uniform-geometric distribution. Journal of Statistical Computation and
Simulation, 86(9), 1754-1770.