logistolint: Logistic (or Log-Logistic) Tolerance Intervals

In dsy109/tolerance: Statistical Tolerance Intervals and Regions

Logistic (or Log-Logistic) Tolerance Intervals

Description

Provides 1-sided or 2-sided tolerance intervals for data distributed according to a logistic or log-logistic distribution.

Usage

logistol.int(x, alpha = 0.05, P = 0.99, log.log = FALSE,
             side = 1, method = c("HALL", "BE"))

Arguments

x	A vector of data which is distributed according to a logistic or log-logistic distribution.
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.
log.log	If TRUE, then the data is considered to be from a log-logistic distribution, in which case the output gives tolerance intervals for the log-logistic distribution. The default is FALSE.
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 tolerance limits. "HALL" is the method due to Hall, which can be numerically unstable (see below for more information). "BE" is the method due to Bain and Englehardt, which is typically more reliable.

Details

Recall that if the random variable X is distributed according to a log-logistic distribution, then the random variable Y = ln(X) is distributed according to a logistic distribution. For method = "HALL", the method due to Hall (1975) is implemented. This, however, can have numerical instabilities due to taking square roots of negative numbers in the calculation, thus leading to two-sided tolerance limits where the upper tolerance limit is smaller than the lower tolerance limit. method = "BE" calculates the limits using the method due to Bain and Englehardt (1991), which tends to be more reliable.

Value

logistol.int returns a data frame with items:

alpha	The specified significance level.
P	The proportion of the population covered by this tolerance interval.
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

Bain, L. and Englehardt, M. (1991), Statistical Analysis of Reliability and Life Testing Models: Theory and Methods, Second Edition, Marcel Dekker, Inc.

Balakrishnan, N. (1992), Handbook of the Logistic Distribution, Marcel Dekker, Inc.

Hall, I. J. (1975), One-Sided Tolerance Limits for a Logistic Distribution Based on Censored Samples, Biometrics, 31, 873–880.

See Also

Logistic

Examples

 
## 90%/95% 1-sided logistic tolerance intervals for a sample
## of size 20. 

set.seed(100)
x <- rlogis(20, 5, 1)
out <- logistol.int(x = x, alpha = 0.10, P = 0.95, 
                    log.log = FALSE, side = 1) 
out

plottol(out, x, plot.type = "control", side = "two", 
        x.lab = "Logistic Data")

dsy109/tolerance documentation built on June 23, 2024, 3:42 a.m.