Parameter estimation of the hybrid censored log-normal distribution

Abstract

The two most common censoring schemes used in life-testing experiments are Type-I and Type-II censoring schemes. The hybrid censoring scheme is mixture of Type-I and Type-II censoring schemes. In this work, we consider the estimation of parameters of log-normal distribution based on hybrid censored data. The parameters are estimated by the maximum likelihood method. It is observed that the maximum likelihood estimates cannot be obtained in a closed form. We obtain the maximum likelihood estimates of the unknown parameters using EM algorithm. We also propose approximate maximum likelihood estimates and these can be used as initial estimates for any iterative procedure. The Fisher information matrix has been obtained and it can be used for constructing asymptotic confidence intervals. The method of obtaining optimum censoring scheme is discussed. One data set is analysed for illustrative purposes.

Keywords:

• maximum likelihood estimators
• EM algorithm
• Type-I censoring
• Type-II censoring
• optimal censoring scheme
• approximate maximum likelihood estimate

Mathematics Subject Classification :

• 62F10
• 62F15
• 62N02

Acknowledgements

The authors would like to thank the referee and the associate editor for constructive suggestions, which has improved the earlier draft of the manuscript. Part of the work of the third author has been supported by a grant from the Department of Science and Technology, Government of India.