xmp06.12 {Devore5}R Documentation

data from Example 6.12

Description

The xmp06.12 data frame has 20 rows and 1 columns of data on the survival times of mice subjected to radiation.

Format

This data frame contains the following columns:

Survival
a numeric vector of survival times (weeks) of mice subjected to 240 rads of gamma radiation.

Details

Source

Devore, J. L. (2000) Probability and Statistics for Engineering and the Sciences (5th ed), Duxbury.

Gross, A. J. and Clark, V. (1976) Survival Distributions: Reliability Applications in the Biomedical Sciences, Wiley.

Examples

data(xmp06.12)
attach(xmp06.12)
gamma.MoM <- function(x) {
   ## calculate method of moments estimates for gamma distribution
   xbar <- mean(x)
   mnSqDev <- mean((x - xbar)^2)
   c(alpha = xbar^2/mnSqDev, beta = mnSqDev/xbar)
}
## method of moments estimates
print(surv.MoM <- gamma.MoM(Survival))
## evaluating the negative log-likelihood
gammaLlik <- function(x) {
   ## argument x is a vector of shape (alpha) and scale (beta)
   -sum(dgamma(Survival, shape = x[1], scale = x[2], log = TRUE))
}
## maximum likelihood estimates - use MoM estimates as starting value
MLE <- optim(par = surv.MoM, gammaLlik)
print(MLE)
detach()