Bootstrap likelihood ratio test for Weibull mixture models fitted to grouped data

Abstract

Weibull mixture models are widely used in a variety of fields for modeling phenomena caused by heterogeneous sources. We focus on circumstances in which original observations are not available, and instead the data comes in the form of a grouping of the original observations. We illustrate EM algorithm for fitting Weibull mixture models for grouped data and propose a bootstrap likelihood ratio test (LRT) for determining the number of subpopulations in a mixture model. The effectiveness of the LRT methods are investigated via simulation. We illustrate the utility of these methods by applying them to two grouped data applications.

Keywords:

• Bootstrap
• EM algorithm
• grouped data
• likelihood ratio test
• Weibull mixture model

Acknowledgments

The authors would like to thank Professor Steven Driese and Lyndsay DiPietro of the Department of Geosciences at Baylor University for providing the grain size data. The stamp thickness data is available in R package BSDA (Arnholt 2012). We would also like to acknowledge two reviewers whose comments improved the manuscript.