exptest (version 1.2)

kimber.exp.test: Kimber-Michael test for exponentiality

Description

Performs Kimber-Michael test for the composite hypothesis of exponentiality, see e.g. Michael (1983), Kimber (1985).

Usage

kimber.exp.test(x, nrepl=2000)

Arguments

x

a numeric vector of data values.

nrepl

the number of replications in Monte Carlo simulation.

Value

• A list with class "htest" containing the following components:
• statistic
  the value of the Kimber-Michael statistic.
• p.value
  the p-value for the test.
• method
  the character string "Kimber-Michael test for exponentiality".
• data.name
  a character string giving the name(s) of the data.

Details

The Kimber-Michael test for exponentiality is based on the following statistic: $$D = \max_i{\left| r_i - s_i\right|},$$ where $$s_i = \frac{2}{\pi} \, \arcsin{\sqrt{1-\exp(-X_{(i)}/\overline{X})}}, \qquad r_i = \frac{2}{\pi} \, \arcsin{\sqrt{(i - 0.5)/n}}.$$ The p-value is computed by Monte Carlo simulation.

References

Kimber, A.C. (1985): Tests for the exponential, Weibull and Gumbel distributions based on the stabilized probability plot. --- Biometrika, vol. 72, pp. 661--663. Michael, J.R. (1983): The stabilized probability plot. --- Biometrika, vol. 70, pp. 11--17.

Examples

kimber.exp.test(rexp(100))
kimber.exp.test(rchisq(100,2))