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

JosŽ-Antonio Esp’n-S‡nchez ()
Additional contact information
JosŽ-Antonio Esp’n-S‡nchez: Cowles Foundation, Yale University, https://cowles.yale.edu/people/jose-antonio-espin-sanchez
Authors registered in the RePEc Author Service: José-Antonio Espín-Sánchez

No 2344, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Pages: 29 pages
Date: 2022-09
References: Add references at CitEc
Citations:

Downloads: (external link)
https://cowles.yale.edu/sites/default/files/2022-11/d2346.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cwl:cwldpp:2346

Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.

Access Statistics for this paper

More papers in Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University Yale University, Box 208281, New Haven, CT 06520-8281 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Brittany Ladd ().