# poislindtolint: Poisson-Lindley Tolerance Intervals In tolerance: Statistical Tolerance Intervals and Regions

## Description

Provides 1-sided or 2-sided tolerance intervals for data distributed according to the Poisson-Lindley distribution.

## Usage

 ```1 2``` ```poislindtol.int(x, m = NULL, alpha = 0.05, P = 0.99, side = 1, ...) ```

## Arguments

 `x` A vector of raw data which is distributed according to a Poisson-Lindley distribution. `m` The number of observations in a future sample for which the tolerance limits will be calculated. By default, `m = NULL` and, thus, `m` will be set equal to the original sample size. `alpha` The level chosen such that 1-alpha is the confidence level. `P` The proportion of the population to be covered by this tolerance interval. `side` Whether a 1-sided or 2-sided tolerance interval is required (determined by `side = 1` or `side = 2`, respectively). `...` Additional arguments passed to the `poislind.ll` function, which is used for maximum likelihood estimation.

## Details

The discrete Poisson-Lindley distribution is a compound distribution that, potentially, provides a better fit for count data relative to the traditional Poisson and negative binomial distributions. Poisson-Lindley distributions are heavily right-skewed distributions. For most practical applications, one will typically be interested in 1-sided upper bounds.

## Value

`poislindtol.int` returns a data frame with the following items:

 `alpha` The specified significance level. `P` The proportion of the population covered by this tolerance interval. `theta` MLE for the shape parameter `theta`. `1-sided.lower` The 1-sided lower tolerance bound. This is given only if `side = 1.` `1-sided.upper` The 1-sided upper tolerance bound. This is given only if `side = 1.` `2-sided.lower` The 2-sided lower tolerance bound. This is given only if `side = 2.` `2-sided.upper` The 2-sided upper tolerance bound. This is given only if `side = 2.`

## References

Naghizadeh Qomi, M., Kiapour, A., and Young, D. S. (2015), Approximate Tolerance Intervals for the Discrete Poisson-Lindley Distribution, Journal of Statistical Computation and Simulation, 86, 841–854.

`PoissonLindley`, `poislind.ll`
 ```1 2 3 4 5 6 7``` ```## 90%/90% 1-sided tolerance intervals for data assuming ## the Poisson-Lindley distribution. x <- c(rep(0, 447), rep(1, 132), rep(2, 42), rep(3, 21), rep(4, 3), rep(5, 2)) out <- poislindtol.int(x, alpha = 0.10, P = 0.90, side = 1) out ```