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 $$x=0,1,...,~\theta >0~and~\lambda =e^{-\theta }.$$