# dparetoll: Maximum Likelihood Estimation for the Discrete Pareto... In tolerance: Statistical Tolerance Intervals and Regions

## Description

Performs maximum likelihood estimation for the parameter of the discrete Pareto distribution.

## Usage

 `1` ```dpareto.ll(x, theta = NULL, ...) ```

## Arguments

 `x` A vector of raw data which is distributed according to a Poisson-Lindley distribution. `theta` Optional starting value for the parameter. If `NULL`, then the method of moments estimator is used. `...` Additional arguments passed to the `mle` function.

## Details

The discrete Pareto distribution is a discretized of the continuous Type II Pareto distribution (also called the Lomax distribution).

## Value

See the help file for `mle` to see how the output is structured.

## References

Krishna, H. and Pundir, P. S. (2009), Discrete Burr and Discrete Pareto Distributions, Statistical Methodology, 6, 177–188.

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.

`mle`, `DiscretePareto`

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```## Maximum likelihood estimation for randomly generated data ## from the discrete Pareto distribution. set.seed(100) dp.data <- rdpareto(n = 500, theta = 0.2) out.dp <- dpareto.ll(dp.data) stats4::coef(out.dp) stats4::vcov(out.dp) ```

### 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