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Order Statistics from Independent Non-Identical Exponentiated and Proportional Hazard Rate Random Variables

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Abstract

We study order statistics (OS) from independent non identically distributed (INID) samples for two large classes of statistical distributions: Exponentiated Distributions (ED) and Proportional Hazard Rate Models (PHRM). We show that for the analytical solution for the CDF (PDF) of OSs in ED and PHRM: i) each OS's CDF (PDF) depends on all shape parameters; ii) the CDF (PDF) of each OS is a weighted average of CDF (PDF) within the same family and with shape parameters equal to a partial sum of the original shape parameters; and iii) the weights are integers and sum up to 1. These properties allows for a clear analytical solution and allows a simple parameter estimation in these classes of distributions.

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  • JosŽ-Antonio Esp’n-S‡nchez, 2022. "Order Statistics from Independent Non-Identical Exponentiated and Proportional Hazard Rate Random Variables," Cowles Foundation Discussion Papers 2344, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2346
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