Characterizations of the power distribution by record values

Proceedings Mathematical Sciences

Min-Young Lee¹ 

[1] Department of Mathematics, Dankook University, Cheonan 0-, Korea$$

关键词: Characterizations;    power distribution;    independent and identically distributed;    hazard rate;    lower record values;    theory of functional equations.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let ${ X_n, n geq 1}$ be a sequence of i.i.d. random variables which has absolutely continuous distribution function $F(x)$ with probability density function $f(x)$ and $F(0) = 0$. Assume that $X_n$ belongs to the class $C^ast_1$ or $C_2$. Then $X_k$ has the power distribution if and only if $X_k$ and $frac{X_{L(n+1)}}{X_{L(n)}}$ or $frac{X_{L(n+1)}}{X_{L(n)}}$ and $frac{X_{L(n)}}{X_{L(n--1)}}$ are identically distributed, respectively. Suppose that $X_n$ belongs to the class $C_3$. Also, $X_k$ has the power distribution if and only if $X_{L(n+1)}$ and $X_{L(n)}cdot V$ are identically distributed, where $V$ is independent of $X_{L(n)}$ and $X_{L(n+1)}$ and is distributed as $X_n$’s.

【 授权许可】

Unknown