Goodness of fit test for the generalized Rayleigh distribution with unknown parameters

Abstract

The use of goodness-of-fit test based on Anderson–Darling (AD) statistic is discussed, with reference to the composite hypothesis that a sample of observations comes from a generalized Rayleigh distribution whose parameters are unspecified. Monte Carlo simulation studies were performed to calculate the critical values for AD test. These critical values are then used for testing whether a set of observations follows a generalized Rayleigh distribution when the scale and shape parameters are unspecified and are estimated from the sample. Functional relationship between the critical values of AD is also examined for each shape parameter (α), sample size (n) and significance level (γ). The power study is performed with the hypothesized generalized Rayleigh against alternate distributions.

Keywords:

• Anderson–Darling test
• generalized Rayleigh
• maximum likelihood
• Monte Carlo simulation
• power function

Acknowledgements

The author thanks the editor and referees for their many helpful suggestions and valuable comments for improving this paper.