Volume 18, Issue 2, June 2019, Pages 123 - 128
Some Characterization Results Based on the Mean Vitality Function of the First-Order Statistics
Authors
A. Toomaj1, *, A. Shirvani2
1Department of Mathematics and Statistics, Gonbad Kavous University, Gonbad Kavous, Iran
2Faculty of Basic Sciences and Engineering, Department of Statistics, Velayat University, Iranshahr, Iran
*Corresponding author. Email: ab.toomaj@gmail.com
Corresponding Author
A. Toomaj
Received 20 February 2016, Accepted 2 January 2018, Available Online 18 June 2019.
- DOI
- 10.2991/jsta.d.190514.004How to use a DOI?
- Keywords
- MRL; MVF; Proportional hazard rate model; Weibull distribution; Mixed system; Stochastic orders
- Abstract
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.
- Copyright
- © 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/).
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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 -