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Likelihood ratio comparisons and logconvexity properties of p-spacings from generalized order statistics

Published online by Cambridge University Press:  25 November 2021

Mahdi Alimohammadi Open the ORCID record for Mahdi Alimohammadi [Opens in a new window] ,
Maryam Esna-Ashari Open the ORCID record for Maryam Esna-Ashari [Opens in a new window]  and
Jorge Navarro Open the ORCID record for Jorge Navarro [Opens in a new window]
Mahdi Alimohammadi*
Affiliation:
Department of Statistics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran.
Maryam Esna-Ashari
Affiliation:
Insurance Research Center, Tehran, Iran.
Jorge Navarro
Affiliation:
Facultad de Matemáticas, Universidad de Murcia, Murcia, Spain
*
*Corresponding author. E-mail: m.alimohammadi@alzahra.ac.ir
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Abstract

Due to the importance of generalized order statistics (GOS) in many branches of Statistics, a wide interest has been shown in investigating stochastic comparisons of GOS. In this article, we study the likelihood ratio ordering of $p$-spacings of GOS, establishing some flexible and applicable results. We also settle certain unresolved related problems by providing some useful lemmas. Since we do not impose restrictions on the model parameters (as previous studies did), our findings yield new results for comparison of various useful models of ordered random variables including order statistics, sequential order statistics, $k$-record values, Pfeifer's record values, and progressive Type-II censored order statistics with arbitrary censoring plans. Some results on preservation of logconvexity properties among spacings are provided as well.

Keywords

Generalized order statisticsk-out-of-n systemsLogconcavity and logconvexityProgressive Type-II censored order statisticsRecord valuesTotal positivity
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 1 , January 2023 , pp. 86 - 105
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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