Inequalities for a distribution with monotone hazard rate期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Inequalities for a distribution with monotone hazard rate

Authors:	Ryoichi Shimizu

Abstract:	Summary LetX be a positive random variable with the survival function $\bar F$ and the densityf. LetX have the moments μ=E(X) and μ₂=E(X ²) and put ε=\|1-μ₂/2μ²\|. Put $q(x) = f(x)/\bar F(x)$ and $q_1 (x) = \bar F(x)/\int_x^\infty {\bar F(u)du}$ . It is proved that the following inequalities hold: $\|\bar F(x) - e^{ - x/\mu } \| \leqq \varepsilon /(1 - \varepsilon e)$ , for allx>0, ifq(x) is monotone and that $\int_0^\infty {\|\bar F(x) - e^{ - x/\mu } \|} dx \leqq 2\varepsilon \mu$ , ifq ₁ (x) is monotone. It is also shown that Brown's inequality $\|\bar F(x) - e^{ - x/\mu } \| \leqq \varepsilon /(1 - \varepsilon )$ which holds wheneverq ₁ (x) is increasing is not valid in general whenq ₁ is decreasing. The Institute of Statistical Mathematics

Keywords:	Characterization exponential distribution hazard rate mean residual life
本文献已被 SpringerLink 等数据库收录！