Density, distribution function, quantile function and random generation for the discrete Lindley distribution.
Usage
ddLd1(x, theta, log = FALSE)
pdLd1(q, theta, lower.tail = TRUE, log.p = FALSE)
qdLd1(p, theta, lower.tail = TRUE)
rdLd1(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
ddLd1 gives the density, pdLd1 gives the distribution
function, qdLd1 gives the quantile function and rdLd1 generates
random deviates.
Details
The Discrete Lindley distribution with a parameter \(\theta\), has density $$f\left( x\right) =\frac{\lambda ^{x}}{1-\log \lambda } \left( \lambda \log\lambda +\left( 1-\lambda \right) \left( 1-\log \lambda^{x+1}\right)\right), $$ where $$x=0,1,...,~\theta >0~and~\lambda =e^{-\theta }.$$