poislindtol.int: Poisson-Lindley Tolerance Intervals

Description

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

Usage

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

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.

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.

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.

Examples

Run this code

## 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

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