poislindtol.int {tolerance}

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, 
                ...) 

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.

See Also

PoissonLindley, poislind.ll

Examples

## 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