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)
Value
ddLd1 gives the density, pdLd1 gives the distribution
function, qdLd1 gives the quantile function and rdLd1 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 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
$$x=0,1,...,~\theta >0~and~\lambda =e^{-\theta }.$$
References
Gómez-Déniz, E. ve Calderín-Ojeda, E., 2011,
The discrete Lindley distribution: properties and applications.Journal of
statistical computation and simulation, 81 (11), 1405-1416.