Estimation of Parameters of Mixed Failure Time Distribution Based on an Extended Modified Sampling Scheme

Abstract

The problem of estimation of parameters of a mixture of degenerate (at zero) and exponential distribution is considered by Dixit and Prasad [Dixit, V. U. (Nee: Jayade, V. D.), Prasad, M. S. (1990). Estimation of parameters of mixed failure time distribution. Commun.in Statist.-Theory Meth., 19(12):4667–4678]. The sampling scheme proposed in it is extended to k positive observations in Dixit [Dixit, V. U. (1993). Statistical Inference for AR (1) Process with Mixed Errors. Unpublished Ph.D. thesis, Shivaji University Kolhapur, India] and moment estimator, MLE and UMVUE based on it are obtained and their finite sample and asymptotic properties are studied. These results are presented in this paper. It is interesting to mention that the sampling scheme proposed by Shinde and Shanubhogue [Shinde, R. L., Shanubhogue, A. (2000). Estimation of parameters and the mean life of a mixed failure time distribution. Commun. Statist.-Theory Meth. 29(11):2621–2642] is a particular case of the sampling scheme proposed in Dixit [Dixit, V. U. (1993). Statistical Inference for AR (1) Process with Mixed Errors. Unpublished Ph.D. thesis, Shivaji University Kolhapur, India] for n = k.

Keywords:

• Maximum likelihood estimator
• UMVUE
• Mixed failure time distribution

Acknowledgments

Author wishes to thank Prof. Y.S. Sathe and the referee for helpful comments and suggestions.