Testing the number of components of the mixture of two inverse Weibull distributions

Abstract

In this paper, we use the likelihood ratio test (LRT) for testing the number of components in a mixture of two inverse Weibull distributions (MTIWD). First, we formulate the null distribution of the likelihood ratio statistic. Next, we calculate the percentage points of the test statistic under two different stopping criteria. In addition, we compute the power of the proposed test under these two stopping criteria and show that global maximization of the likelihood is not necessary to obtain a good power of the LRT. Finally, we discuss two applications to illustrate whether a set of data arises from a single or a MTIWD.

Keywords:

• finite mixtures
• EM algorithm
• Monte Carlo method
• likelihood ratio test
• percentage points and power

AMS Subject Classification :

• 62-07
• 62F03
• 62F10

Acknowledgements

The authors would like to thank the referees for their helpful comments, which improved the presentation of the paper.