# dparetotolint: Discrete Pareto Tolerance Intervals In tolerance: Statistical Tolerance Intervals and Regions

## Description

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

## Usage

 ```1 2``` ```dparetotol.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 discrete Pareto 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 `dpareto.ll` function, which is used for maximum likelihood estimation.

## Details

The discrete Pareto is a discretized of the continuous Type II Pareto distribution (also called the Lomax distribution). Discrete Pareto distributions are heavily right-skewed distributions and potentially good models for discrete lifetime data and extremes in count data. For most practical applications, one will typically be interested in 1-sided upper bounds.

## Value

`dparetotol.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

Young, D. S., Naghizadeh Qomi, M., and Kiapour, A. (2019), Approximate Discrete Pareto Tolerance Limits for Characterizing Extremes in Count Data, Statistica Neerlandica, 73, 4–21.

`DiscretePareto`, `dpareto.ll`
 ```1 2 3 4 5 6 7 8``` ```## 95%/95% 1-sided tolerance intervals for data assuming ## the discrete Pareto distribution. set.seed(100) x <- rdpareto(n = 500, theta = 0.5) out <- dparetotol.int(x, alpha = 0.05, P = 0.95, side = 1) out ```