Proceedings Mathematical Sciences | |
Characterizations of the power distribution by record values | |
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
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO201912040507198ZK.pdf | 58KB | download |