Estimation of the Bivariate Kumaraswamy Lifetime Distribution under Progressive Type-I Censoring

Hanan. M. Aly ； Hiba. Z. Muhammed ； Ola. A. Abuelamayem

《Journal of Data Science》 18卷4期 (2020/10) Pp. 739-749

https://doi.org/10.6339/JDS.202010_18(4).0009

摘要

Analyzing time to event data arises in a number of fields such as Biology and Engineering. A common feature of this data is that, the exact failure time for all units may not be observable. Accordingly, several types of censoring were presented. Progressive censoring allows units to be randomly removed before the terminal point of the experiment. Marshall-Olkin bivariate lifetime distribution was first introduced in 1967 using the exponential distribution. Recently, bivariate Marshall-Olkin Kumaraswamy lifetime distribution was derived. This paper derives the likelihood function under progressive type-I censoring for the bivariate Marshall-Olkin family in general and applies it on the bivariate Kumaraswamy lifetime distribution. Maximum likelihood estimators of model parameters were derived. Simulation study and a real data set are presented to illustrate the proposed procedure. Absolute bias, mean square error, asymptotic confidence intervals, confidence width and coverage probability are obtained. Simulation results indicate that the mean square error is smaller and confidence width is narrower and more precise when number of removals gets smaller. Also, increasing the terminal point of the experiment results in reducing the mean square error and confidence width.

關鍵字

bivariate Marshall-Olkin ； maximum likelihood estimation