gamtol.int {tolerance}R Documentation

Gamma (or Log-Gamma) Tolerance Intervals

Description

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

Usage

gamtol.int(x, alpha = 0.05, P = 0.99, side = 1,
           method = c("HE", "WBE"), log.gamma = FALSE)

Arguments

x A vector of data which is distributed according to either a gamma distribution or a log-gamma 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.
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 k-factors when using the normal approximation. The k-factor for the 1-sided tolerance intervals is performed exactly and thus the same for either method chosen. "HE" is the Howe method and is often viewed as being extremely accurate, even for small sample sizes. "WBE" is the Weissberg-Beatty method, which performs similarly to the Howe method for larger sample sizes.
log.gamma If TRUE, then the data is considered to be from a log-gamma distribution, in which case the output gives tolerance intervals for the log-gamma distribution. The default is FALSE.

Details

Recall that if the random variable X is distributed according to a log-gamma distribution, then the random variable Y = ln(X) is distributed according to a gamma distribution.

Value

gamtol.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

Krishnamoorthy, K., Mathew, T., and Mukherjee, S. (2008), Normal-Based Methods for a Gamma Distribution: Prediction and Tolerance Intervals and Stress-Strength Reliability, Technometrics, 50, 69–78.

See Also

GammaDist, K.factor

Examples

 

## 99%/99% 1-sided gamma tolerance intervals for a sample
## of size 50. 

set.seed(100)
x <- rgamma(50, 0.30, scale = 2)
out <- gamtol.int(x = x, alpha = 0.01, P = 0.99, side = 1,
                  method = "HE")
out

plottol(out, x, plot.type = "both", side = "upper", 
        x.lab = "Gamma Data")

[Package tolerance version 0.1.0 Index]