Density, distribution function, quantile function and random generation for the discrete Lindley distribution.
Usage
ddLd2(x, theta, log = FALSE)
pdLd2(q, theta, lower.tail = TRUE, log.p = FALSE)
qdLd2(p, theta, lower.tail = TRUE)
rdLd2(n, theta)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.
Value
ddLd2 gives the density, pdLd2 gives the distribution
function, qdLd2 gives the quantile function and rdLd2 generates
random deviates.
Details
the discrete Lindley distribution with a parameter \(\theta\), has density $$f\left( x\right) =\frac{\lambda ^{x}}{1+\theta } \left( \theta \left(1-2\lambda \right) +\left( 1-\lambda \right) \left( 1+\theta x\right)\right),$$ where $$x=0,1,2,...~,\lambda =\exp \left( -\theta \right) ~and~\theta >0.$$