New tests for exponentiality against new better than used in pth quantile

Abstract

A new characterisation of the exponential distribution in a wide class of new better than used in pth quantile (NBUp) lifetime distributions is presented. This leads to new classes of scale-free goodness-of-fit tests for exponentiality against NBUp alternatives. The limiting distributions of the test statistics under the null and alternative hypotheses are derived and the tests are shown to be consistent against NBUp alternatives. Pitman efficacies are calculated and a limited Monte Carlo study is conducted to compare the tests with regard to power for small and moderate sample sizes against a range of alternative distributions. On the basis of overall good performance and ease of computation, a member of the class of test statistics which is based on the sample Winsorised mean is recommended as a scale-free goodness-of-fit test for the exponential distribution.

Keywords:

• characterisation
• exponential distribution
• hazard rate function
• new better than used in pth quantile
• testing
• U-quantile
• Winsorised mean

2000 Mathematical Subject Classification :

• Primary: 62F03
• Secondary: 62E10
• 62N03
• 62N05

Acknowledgements

The authors are very grateful to Mr James Allison, North-West University for his valuable help with the numerical and simulation work. The first and third author acknowledge support from IUAP Research Network P6/03 of the Belgian government (Belgian Science Policy). The second author thanks the National Research Foundation of South Africa for financial support. All authors acknowledge financial support from the project BOF05B01 of Hasselt University.