gamtol.int {tolerance} | R Documentation |
Provides 1-sided or 2-sided tolerance intervals for data distributed according to either a gamma distribution or log-gamma distribution.
gamtol.int(x, alpha = 0.05, P = 0.99, side = 1, method = c("HE", "WBE"), 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 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 . |
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.
## 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")