Order Statistics from Independent Non-Identical Exponentiated and Proportional Hazard Rate Random Variables
Journal of Economic Literature (JEL) Code(s)
C4, C57, F11, L1
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.
Espín-Sánchez, José-Antonio and Wu, Tianhao, "Order Statistics from Independent Non-Identical Exponentiated and Proportional Hazard Rate Random Variables" (2022). Cowles Foundation Discussion Papers. 2707.