Estimation of parameters of the logistic exponential distribution under progressive type-I hybrid censored sample

ABSTRACT

The present paper addresses the problem of estimation of model parameters of the logistic exponential distribution based on progressive type-I hybrid censored sample. The maximum likelihood estimates are obtained and computed numerically using Newton–Raphson algorithm. Further, the Bayes estimates are derived under the squared error, LINEX and the generalized entropy loss functions. Two types (independent and bivariate) of prior distributions are considered for the purpose of Bayesian estimation. It is seen that the Bayes estimates are not of explicit forms. Thus, Lindley’s approximation technique is employed to get approximate Bayes estimates. Interval estimates of the parameters based on the normal approximation of the maximum likelihood estimates and the log-transformed maximum likelihood estimates are constructed. The highest posterior density credible intervals are obtained by using the importance sampling method. Numerical simulation is performed to see the performance of the proposed estimation techniques. A real-life data set is considered and analysed for the purpose of illustrations.

KEYWORDS:

• Newton–Raphson method
• independent and bivariate priors
• Lindley’s approximation
• importance sampling method
• mean squared error
• coverage probability

Acknowledgments

The authors would like to thank the Editor in Chief, an Associate Editor and anonymous reviewers for their positive remarks and useful comments. The author S. Dutta thanks the Council of Scientific and Industrial Research (C.S.I.R. Grant No. 09/983(0038)/2019-EMR-I), India, for the financial assistantship received to carry out this research work. Both the authors thank the research facilities received from the Department of Mathematics, National Institute of Technology Rourkela, India.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the CSIR [09/983(0038)/2019-EMR-I].