Some Characterization Results Based on the Mean Vitality Function of the First-Order Statistics
- 10.2991/jsta.d.190514.004How to use a DOI?
- MRL; MVF; Proportional hazard rate model; Weibull distribution; Mixed system; Stochastic orders
In this paper, we investigate some new properties of the mean vitality function (MVF) of a random variable, proposed by A. Toomaj, M. Doostparast, J. Stat. Theory Appl. 13 (2013), 189–195. Specifically, we explore properties of MVF and study under what conditions the MVF of the first-order statistics can uniquely determines the parent distribution. We show that in all distributions the Weibull family, which is commonly used in several fields of applied probability, is characterized through the ratio of the MVF of the first-order statistics to its expectation.
- © 2019 The Authors. Published by Atlantis Press SARL.
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - A. Toomaj AU - A. Shirvani PY - 2019 DA - 2019/06/18 TI - Some Characterization Results Based on the Mean Vitality Function of the First-Order Statistics JO - Journal of Statistical Theory and Applications SP - 123 EP - 128 VL - 18 IS - 2 SN - 2214-1766 UR - https://doi.org/10.2991/jsta.d.190514.004 DO - 10.2991/jsta.d.190514.004 ID - Toomaj2019 ER -