Estimation of a discriminant function from a mixture of two inverse Weibull distributions

Abstract

The classification of a random variable based on a mixture can be meaningfully discussed only if the class of all finite mixtures is identifiable. In this paper, we find the maximum-likelihood estimates of the parameters of the mixture of two inverse Weibull distributions by using classified and unclassified observations. Next, we estimate the nonlinear discriminant function of the underlying model. Also, we calculate the total probabilities of misclassification as well as the percentage bias. In addition, we investigate the performance of all results through a series of simulation experiments by means of relative efficiencies. Finally, we analyse some simulated and real data sets through the findings of the paper.

Keywords:

• finite mixtures
• maximum-likelihood estimation
• EM algorithm
• discriminant function
• bias
• mean-square error
• relative efficiency and Monte Carlo simulations

Acknowledgements

The authors thank the referees for their helpful comments, which improved the presentation of the paper. This project was supported by king Saud University, Deanship of Scientific Research, College of Science Research Center.

Additional information

Notes on contributors

A. S. Al-Moisheer

Present address: Department of Mathematics, College of Science, Al-Jouf University, PO Box 2014, Al-Jouf, Sakaka Kingdom of Saudi Arabia.