1. Resolving an open problem on the hazard rate ordering of p -spacings.
- Author
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Alimohammadi, Mahdi
- Subjects
- *
ORDER statistics , *STOCHASTIC orders , *CONTINUOUS distributions , *DISTRIBUTION (Probability theory) , *CONTINUOUS functions - Abstract
Let $V_{(r,n,\tilde {m}_n,k)}^{(p)}$ and $W_{(r,n,\tilde {m}_n,k)}^{(p)}$ be the $p$ -spacings of generalized order statistics based on absolutely continuous distribution functions $F$ and $G$ , respectively. Imposing some conditions on $F$ and $G$ and assuming that $m_1=\cdots =m_{n-1}$ , Hu and Zhuang (2006. Stochastic orderings between p -spacings of generalized order statistics from two samples. Probability in the Engineering and Informational Sciences 20: 475) established $V_{(r,n,\tilde {m}_n,k)}^{(p)} \leq _{{\rm hr}} W_{(r,n,\tilde {m}_n,k)}^{(p)}$ for $p=1$ and left the case $p\geq 2$ as an open problem. In this article, we not only resolve it but also give the result for unequal $m_i$ 's. It is worth mentioning that this problem has not been proved even for ordinary order statistics so far. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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