Likelihood ratio comparisons and logconvexity properties of<i>p</i>-spacings from generalized order statistics

Alimohammadi, Mahdi; Esna-Ashari, Maryam; Navarro, Jorge

doi:10.1017/s0269964821000498

Cited by 4 publications

(2 citation statements)

References 33 publications

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“…is increasing in u. This is carried out proceeding by induction on p. For p = 2, due to (13) we have…”

Section: Stochastic Orders From One Samplementioning

confidence: 99%

Some New Results on Stochastic Comparisons of Spacings of Generalized Order Statistics from One and Two Samples

Esna-Ashari,

Alimohammadi,

Garousi

et al. 2024

Mathematics

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Generalized order statistics (GOSs) are often adopted as a tool for providing a unified approach to several stochastic models dealing with ordered random variables. In this contribution, we first recall various useful results based on the notion of total positivity. Then, some stochastic comparisons between spacings of GOSs from one sample, as well as two samples, are developed under the more general assumptions on the parameters of the model. Specifically, the given results deal with the likelihood ratio order, the hazard rate order and the mean residual life order. Finally, an application is demonstrated for sequential systems.

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“…is increasing in u. This is carried out proceeding by induction on p. For p = 2, due to (13) we have…”

Section: Stochastic Orders From One Samplementioning

confidence: 99%

Some New Results on Stochastic Comparisons of Spacings of Generalized Order Statistics from One and Two Samples

Esna-Ashari,

Alimohammadi,

Garousi

et al. 2024

Mathematics

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“…For one-sample problem of 𝑝-spacings, some stochastic properties of order statistics and GOS have been studied by several authors such as Misra and van der Meulen [21], Hu and Zhuang [13,14], Xie and Hu [25], and Alimohammadi et al [4]. For two-sample problem of 𝑝-spacings, a study of stochastic comparisons was initiated by Kochar [20].…”

Section: Introductionmentioning

confidence: 99%

Resolving an open problem on the hazard rate ordering of p-spacings

Alimohammadi¹

2022

Prob. Eng. Inf. Sci.

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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.

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