tolerance (version 3.0.0)

dparetotol.int: Discrete Pareto Tolerance Intervals

Description

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

Usage

dparetotol.int(x, m = NULL, alpha = 0.05, P = 0.99, side = 1, 
                ...)

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.

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.

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.

See Also

DiscretePareto, dpareto.ll

Examples

## 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