gammatolint: Gamma (or Log-Gamma) Tolerance Intervals
In tolerance: Statistical Tolerance Intervals and Regions

Description Usage Arguments Details Value References See Also Examples

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

1
2
3

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)

`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 for small sample sizes. `"HE2"` is a second method due to Howe, which performs similarly to the Weissberg-Beatty method, but is computationally simpler. `"WBE"` is the Weissberg-Beatty method (also called the Wald-Wolfowitz method), which performs similarly to the first Howe method for larger sample sizes. `"ELL"` is the Ellison correction to the Weissberg-Beatty method when `f` is appreciably larger than `n^2`. A warning message is displayed if `f` is not larger than `n^2`. `"KM"` is the Krishnamoorthy-Mathew approximation to the exact solution, which works well for larger sample sizes. `"EXACT"` computes the k-factor exactly by finding the integral solution to the problem via the `integrate` function. Note the computation time of this method is largely determined by `m`. `"OCT"` is the Owen approach to compute the k-factor when controlling the tails so that there is not more than (1-P)/2 of the data in each tail of the distribution.
`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 can result in an error. A large value can also cause the function to be slow for `method = "EXACT"`.
`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`.

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.

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`.

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.

GammaDist, K.factor

 
## 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")