Some new results on likelihood ratio ordering and aging properties of generalized order statistics

Esna-Ashari, Maryam; Alimohammadi, Mahdi; Cramer, Erhard

doi:10.1080/03610926.2020.1818103

Cited by 8 publications

(5 citation statements)

References 38 publications

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“…According to the method of proof used in Lemma 3.2 of [18], we get that if for , then is decreasing in ; if and for , then is decreasing in .…”

Section: Preliminary Results and Useful Lemmasmentioning

confidence: 99%

“…In another direction, if 𝑓 is logconcave (logconvex), then F is logconcave (logconvex). So, (18) becomes the product of logconcave functions and, therefore, 𝑓 𝑋 * 𝑟 is logconcave as claimed. This is also deduced from Corollary 2.4 of Chen et al [11] where it is stated that the logconcavity of 𝑓 is not sufficient for the logconcavity of record values and that we need a stronger condition that ℎ is logconcave.…”

Section: Counterexample 44 Suppose That 𝑋 Has a Truncated Cauchy Dist...mentioning

confidence: 87%

“…The part (i.a) of the following theorem was established by Karlin [26] and the others by Esna-Ashari et al [18]. It was called the extended basic composition theorem.…”

Section: Definition 21 (Barlow and Proschan [7]) A Function 𝜆mentioning

confidence: 99%

“…This enables us to compare the -spacings of submodels of GOS among themselves. More generally, we can compare the -spacings obtained from different submodels (we refer the reader to Franco et al [20], Belzunce et al [9], Esna-Ashari et al [18] and Alimohammadi et al [4], for some stochastic orderings of GOS with different parameters and ). Specifically, we extend ()–() in the unifying Theorem 3.1 for different parameters and .…”

Section: Introductionmentioning

confidence: 99%

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

Alimohammadi

Esna-Ashari²,

Navarro

2021

Prob. Eng. Inf. Sci.

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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.

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“…According to the method of proof used in Lemma 3.2 of [18], we get that if for , then is decreasing in ; if and for , then is decreasing in .…”

Section: Preliminary Results and Useful Lemmasmentioning

confidence: 99%

Section: Counterexample 44 Suppose That 𝑋 Has a Truncated Cauchy Dist...mentioning

confidence: 87%

“…The part (i.a) of the following theorem was established by Karlin [26] and the others by Esna-Ashari et al [18]. It was called the extended basic composition theorem.…”

Section: Definition 21 (Barlow and Proschan [7]) A Function 𝜆mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Alimohammadi

Esna-Ashari²,

Navarro

2021

Prob. Eng. Inf. Sci.

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“…The reinterpretation of elasticity in statistical terms and its better comprehension Pavía 2012, 2014) has indirectly expanded the use of (proportional) reserve hazard rates and has directly opened up new areas for their application. In addition to fostering their classical usefulness in survival analysis and stochastic ordering (see, e.g., Navarro et al 2014;Oliveira and Torrado 2015;Balakrishnan et al 2017;Kundu and Ghosh 2017;Hazra et al 2017;Arab and Oliveira 2019;Esna-Ashari et al 2020), they are being applied to new areas, such as epidemiology (Veres-Ferrer and Pavía 2021), risk management in business (Pavía et al 2012;Torrado and Oliviera 2013;Pavía and Veres-Ferrer 2016;Torrado and Navarro 2021), and trading and bidding in markets (Yang et al 2021;Auster and Kellner 2022). Furthermore, these tools are proving their usefulness in the field of medicine (Popović et al 2021), for the characterisation of stochastic distributions Pavía 2017a, 2017b) and as a means for proposing new probability models (Szymkowiak 2019;Kotelo 2019;Anis and De 2020).…”

Section: Introductionmentioning

confidence: 99%

The Elasticity of a Random Variable as a Tool for Measuring and Assessing Risks

Veres-Ferrer

Pavía

2022

Risks

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Elasticity is a very popular concept in economics and physics, recently exported and reinterpreted in the statistical field, where it has given form to the so-called elasticity function. This function has proved to be a very useful tool for quantifying and evaluating risks, with applications in disciplines as varied as public health and financial risk management. In this study, we consider the elasticity function in random terms, defining its probability distribution, which allows us to measure for each stochastic process the probability of finding elastic or inelastic situations (i.e., with elasticities greater or less than 1). This new tool, together with new results on the most notable points of the elasticity function covered in this research, offers a new approach to risk assessment, facilitating proactive risk management. The paper also includes other contributions of interest, such as new results that relate elasticity and inverse hazard functions, the derivation of the functional form of the cumulative distribution function of a probability model with constant elasticity and how the elasticities of functionally dependent variables are related. The interested reader can also find in the paper examples of how elasticity cumulative distribution functions are calculated, and an extensive list of probability models with their associated elasticity functions and distributions.

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HR and RHR orderings of generalized order statistics

Esna-Ashari¹,

Alimohammadi

2022

Metrika

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Some new results on likelihood ratio ordering and aging properties of generalized order statistics

Cited by 8 publications

References 38 publications

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

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

The Elasticity of a Random Variable as a Tool for Measuring and Assessing Risks

HR and RHR orderings of generalized order statistics

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