poistol.int: Poisson Tolerance Intervals

Description

Provides 1-sided or 2-sided tolerance intervals for Poisson random variables. From a statistical quality control perspective, these limits bound the number of occurrences (which follow a Poisson distribution) in a specified future time period.

Usage

poistol.int(x, n, m, alpha = 0.05, P = 0.99, side = 1, 
            method = c("TAB", "LS", "SC"))

Arguments

The number of occurrences of the event in time period n. Can be a vector of length n, in which case the sum of x is used.

The time period of the original measurements.

The specified future length of time.

alpha

The level chosen such that 1-alpha is the confidence level.

The proportion of occurrences in future time lengths of size m 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).

method

The method for calculating the lower and upper confidence bounds, which are used in the calculation of the tolerance bounds. The default method is "TAB", which is the tabular method and is usually preferred for a smaller number of occu

Value

poistol.int returns a data frame with items:
alphaThe specified significance level.
PThe proportion of occurrences in future time periods of length m.
lambda.hatThe mean occurrence rate per unit time, calculated by x/n.
1-sided.lowerThe 1-sided lower tolerance bound. This is given only if side = 1.
1-sided.upperThe 1-sided upper tolerance bound. This is given only if side = 1.
2-sided.lowerThe 2-sided lower tolerance bound. This is given only if side = 2.
2-sided.upperThe 2-sided upper tolerance bound. This is given only if side = 2.

References

Hahn, G. J. and Chandra, R. (1981), Tolerance Intervals for Poisson and Binomial Variables, Journal of Quality Technology, 13, 100--110.

Examples

Run this code

## 95%/90% 1-sided Poisson tolerance limits for future 
## occurrences in a period of length 3.  All three methods
## are presented for comparison.

poistol.int(x = 45, n = 9, m = 3, alpha = 0.05, P = 0.90,
            side = 1, method = "TAB")
poistol.int(x = 45, n = 9, m = 3, alpha = 0.05, P = 0.90,
            side = 1, method = "LS")
poistol.int(x = 45, n = 9, m = 3, alpha = 0.05, P = 0.90,
            side = 1, method = "SC")

## 95%/90% 2-sided Poisson tolerance intervals for future 
## occurrences in a period of length 15.  All three methods
## are presented for comparison.

poistol.int(x = 45, n = 9, m = 15, alpha = 0.05, P = 0.90,
            side = 2, method = "TAB")
poistol.int(x = 45, n = 9, m = 15, alpha = 0.05, P = 0.90,
            side = 2, method = "LS")
poistol.int(x = 45, n = 9, m = 15, alpha = 0.05, P = 0.90,
            side = 2, method = "SC")