# DPLindley: Discrete Power Lindley Distribution In LindleyR: The Lindley Distribution and Its Modifications

## Description

Probability mass function, distribution function, quantile function and random number generation for the discrete power Lindley distribution with parameters theta and alpha.

## Usage

 1 2 3 4 5 6 7 ddplindley(x, theta, alpha, log = FALSE) pdplindley(q, theta, alpha, lower.tail = TRUE, log.p = FALSE) qdplindley(p, theta, alpha, lower.tail = TRUE, log.p = FALSE) rdplindley(n, theta, alpha) 

## Arguments

 x, q vector of integer positive quantiles. theta, alpha positive parameter. log, log.p logical; If TRUE, probabilities p are given as log(p). lower.tail logical; If TRUE, (default), P(X ≤q x) are returned, otherwise P(X > x). p vector of probabilities. n number of observations. If length(n) > 1, the length is taken to be the number required.

## Details

Probability mass function

P(X=x\mid θ ,α )=∑\limits_{i=0}^{1}≤ft( -1\right) ^{i}≤ft( 1+{\frac{θ }{θ +1}}≤ft( x+i\right) ^{α }\right) \ e^{-θ ≤ft( x+i\right) ^{α}}

Particular case: α = 1 the one-parameter discrete Lindley distribution.

## Value

ddplindley gives the probability mass function, pdplindley gives the distribution function, qdplindley gives the quantile function and rdplindley generates random deviates.

Invalid arguments will return an error message.

## Author(s)

Josmar Mazucheli jmazucheli@gmail.com

Ricardo P. de Oliveira rpuziol.oliveira@gmail.com

## Source

[d-p-q-r]dplindley are calculated directly from the definitions. rdplindley uses the discretize values.

## References

Ghitany, M. E., Al-Mutairi, D. K., Balakrishnan, N. and Al-Enezi, L. J., (2013). Power Lindley distribution and associated inference. Computational Statistics and Data Analysis, 64, 20-33.

Mazucheli, J., Ghitany, M. E. and Louzada, F., (2013). Power Lindley distribution: Diferent methods of estimation and their applications to survival times data. Journal of Applied Statistical Science, 21, (2), 135-144.

PLindley.
  1 2 3 4 5 6 7 8 9 10 11 set.seed(1) x <- rdplindley(n = 1000, theta = 1.5, alpha = 0.5) plot(table(x) / sum(table(x))) points(unique(x),ddplindley(unique(x), theta = 1.5, alpha = 0.5)) ## fires in Greece data (from Bakouch et al., 2014) data(fires) library(fitdistrplus) fit <- fitdist(fires, 'dplindley', start = list(theta = 0.30, alpha = 1.0), discrete = TRUE) gofstat(fit, discrete = TRUE) plot(fit)