# poislind: Discrete Poisson-Lindley Distribution In tolerance: Statistical Tolerance Intervals and Regions

## Description

Density (mass), distribution function, quantile function, and random generation for the Poisson-Lindley distribution.

## Usage

 ```1 2 3 4``` ```dpoislind(x, theta, log = FALSE) ppoislind(q, theta, lower.tail = TRUE, log.p = FALSE) qpoislind(p, theta, lower.tail = TRUE, log.p = FALSE) rpoislind(n, theta) ```

## Arguments

 `x, q` Vector of quantiles. `p` Vector of probabilities. `n` The number of observations. If `length>1`, then the length is taken to be the number required. `theta` The shape parameter, which must be greater than 0. `log, log.p` Logical vectors. If `TRUE`, then the probabilities are given as `log(p)`. `lower.tail` Logical vector. If `TRUE`, then probabilities are P[X≤ x], else P[X>x].

## Details

The Poisson-Lindley distribution has mass

p(x) = (θ^2(x + θ + 2))/(θ + 1)^(x+3),

where x=0,1,… and θ>0 is the shape parameter.

## Value

`dpoislind` gives the density (mass), `ppoislind` gives the distribution function, `qpoislind` gives the quantile function, and `rpoislind` generates random deviates for the specified distribution.

## References

Ghitany, M. E. and Al-Mutairi, D. K. (2009), Estimation Methods for the Discrete Poisson-Lindley Distribution, Journal of Statistical Computation and Simulation, 79, 1–9.

Sankaran, M. (1970), The Discrete Poisson-Lindley Distribution, Biometrics, 26, 145–149.

`runif` and `.Random.seed` about random number generation.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```## Randomly generated data from the Poisson-Lindley ## distribution. set.seed(100) x <- rpoislind(n = 150, theta = 0.5) hist(x, main = "Randomly Generated Data", prob = TRUE) x.1 <- sort(x) y <- dpoislind(x = x.1, theta = 0.5) lines(x.1, y, col = 2, lwd = 2) plot(x.1, ppoislind(q = x.1, theta = 0.5), type = "l", xlab = "x", ylab = "Cumulative Probabilities") qpoislind(p = 0.20, theta = 0.5, lower.tail = FALSE) qpoislind(p = 0.80, theta = 0.5) ```

### Example output  ```Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE