Moments of Order Statistics from Nonidentically Distributed Three Parameters Beta typeI and Erlang Truncated Exponential Variables

Problem statement: Moments of order statistics of independent non-identically distributed (INID) random variables is not an easy subject to deal with for continuous distributions. One is forced to use messy algebraic calculations (whether one uses permanents or not). This was the motivation behind this study. In this study the moments of order statistics arising from independent nonidentically distributed three parameters Beta type I distribution and Erlang Truncated Exponential distribution were derived. Approach: We employed an easier technique established by Barakat & Abdelkader will be referred to as (BAT). Results: The mean, the second moment and the variance of the median and the smallest order statistics for the first distribution were given for different values of the shape parameter and different sample sizes. Conclusion: The results can be used to make some inferences and used the BAT technique to derive moments of order statistics arising from independent nonidentically distributed for any other continuous distribution with distribution function (cdf) in the form: F(x) = 1-λ (x).