ks.expo.weibull: Test of Kolmogorov-Smirnov for the Exponentiated Weibull(EW)...

In reliaR: Comprehensive Tools for some Probability Distributions

Test of Kolmogorov-Smirnov for the Exponentiated Weibull(EW) distribution

Description

The function ks.expo.weibull() gives the values for the KS test assuming a Exponentiated Weibull(EW) with shape parameter alpha and scale parameter theta. In addition, optionally, this function allows one to show a comparative graph between the empirical and theoretical cdfs for a specified data set.

Usage

ks.expo.weibull(x, alpha.est, theta.est, 
    alternative = c("less", "two.sided", "greater"), plot = FALSE, ...)

Arguments

x	vector of observations.
alpha.est	estimate of the parameter alpha
theta.est	estimate of the parameter theta
alternative	indicates the alternative hypothesis and must be one of "two.sided" (default), "less", or "greater".
plot	Logical; if TRUE, the cdf plot is provided.
...	additional arguments to be passed to the underlying plot function.

Details

The Kolmogorov-Smirnov test is a goodness-of-fit technique based on the maximum distance between the empirical and theoretical cdfs.

Value

The function ks.expo.weibull() carries out the KS test for the Exponentiated Weibull(EW)

References

Mudholkar, G.S. and Srivastava, D.K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42(2), 299-302.

Murthy, D.N.P., Xie, M. and Jiang, R. (2003). Weibull Models, Wiley, New York.

Nassar, M.M., and Eissa, F. H. (2003). On the Exponentiated Weibull Distribution, Communications in Statistics - Theory and Methods, 32(7), 1317-1336.

See Also

pp.expo.weibull for PP plot and qq.expo.weibull for QQ plot

Examples

## Load data sets
data(stress)
## Maximum Likelihood(ML) Estimates of alpha & theta for the data(stress)
## Estimates of alpha & theta using 'maxLik' package
## alpha.est =1.026465, theta.est = 7.824943

ks.expo.weibull(stress, 1.026465, 7.824943, alternative = "two.sided", plot = TRUE)

reliaR documentation built on Nov. 5, 2025, 6:57 p.m.