# DLindley: One-Parameter Discrete Lindley Distribution In LindleyR: The Lindley Distribution and Its Modifications

## Description

Probability mass function, distribution function, quantile function and random number generation for the one-parameter discrete Lindley distribution with parameter theta.

## Usage

 1 2 3 4 5 6 7 ddlindley(x, theta, log = FALSE) pdlindley(q, theta, lower.tail = TRUE, log.p = FALSE) qdlindley(p, theta, lower.tail = TRUE, log.p = FALSE) rdlindley(n, theta) 

## Arguments

 x, q vector of integer positive quantiles. theta 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≤ft( X=x\mid θ \right) =∑\limits_{i=0}^{1}≤ft( -1\right) ^{i}≤ft( 1+\frac{θ }{1+θ }≤ft( x+i\right) \right) e^{-θ ≤ft( x+i\right) }

## Value

ddlindley gives the probability mass function, pdlindley gives the distribution function, qdlindley gives the quantile function and rdlindley generates random deviates.

Invalid arguments will return an error message.

## Author(s)

Josmar Mazucheli jmazucheli@gmail.com

Larissa B. Fernandes lbf.estatistica@gmail.com

## Source

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

## References

Bakouch, H. S., Jazi, M. A. and Nadarajah, S. (2014). A new discrete distribution. Statistics: A Journal of Theoretical and Applied Statistics, 48, 1, 200-240.

Gomez-Deniz, E. and Calderín-Ojeda, E. (2013). The discrete Lindley distribution: properties and applications. Journal of Statistical Computation and Simulation, 81, 11, 1405-1416.

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