## Expected Experiment Times for Burr Type XII Distribution Under Progressive Censoring With Random Removals

### by Abd Allah A. Abd Elghaly, Abd-Elfattah A. M. and Assar S. M.

**Abstract:**
In this paper, the estimation problem for the unknown parameters of the Burr type XII distribution based on progressive type-II censoring with random removals is considered, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the unknown parameters and the asymptotic variance-covariance matrix of the estimates are obtained. Also, the expected experiment times for the Burr type XII distribution under progressive type-II censoring with binomial removals is considered. Furthermore, the ratio of the expected experiment time under type II progressive censoring to the expected experiment time under complete sampling is studied. Finally, numerical examples are given to illustrate some of the theoretical results.
**Key Words: **
Binomial removals; Burr type XII distribution; Expected experiment time; Maximum likelihood estimation; Type-II Progressive censoring; Variance covariance matrix

**Authors:**

Abd Allah A. Abd Elghaly, abdelghaly@yahoo.com

Abd-Elfattah,A.M., a_afattah@hotmail.com

Assar S. M., salwaassar@yahoo.com

**Editor:**
sanku dey, sanku_dey2k2003@yahoo.co.in

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