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.