Estimation under Burr type X distribution based on doubly type II censored sample of dual generalized order statistics

Document Type : Original Article

Authors

1 Dept. of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt

2 Dept. of Mathematics and Statistics, Faculty of Science, Helwan University, Ain Helwan, Cairo, Egypt1

3 Dept. of Mathematics, Faculty of Science, Taibah University, Madinah, Saudi Arabia

4 Dept. of Mathematics and Statistics, Faculty of Science, Taif University, Taif, Saudi Arabia

Abstract

In this paper, maximum likelihood and Bayes estimates of the parameters for Burr type
X distribution based on doubly type II censored sample of dual generalized order statistics are
obtained. Two different cases are considered. In the first case, the shape parameter is estimated
when the scale parameter is known while in the second case the estimators for scale and shape
parameters are obtained when both parameters are assumed to be unknown. For Bayesian estimation, Monte Carlo Integration is used to improve the approximation of resulting integrals. Simulation studies are conducted to demonstrate the efficiency of the proposed methods through two
special cases.

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