tolerance (version 1.1.1)

gamtol.int: 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", "HE2", "WBE", "ELL", "KM", "EXACT", 
           "OCT"), m = 50, 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. The k-factor for the 1-sided tolerance intervals is performed exactly and thus is the same for the chosen method. "HE" is the Howe method and is often viewed as being extremely accurate, even

m

The maximum number of subintervals to be used in the integrate function. This is necessary only for method = "EXACT" and method = "OCT". The larger the number, the more accurate the solution. Too low of a value

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.

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.

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.

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")