Further Results on Quantile Entropy in the Past Lifetime

Qiu, Guoxin

doi:10.1017/s0269964818000062

Cited by 9 publications

(3 citation statements)

References 34 publications

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“…Stochastic comparisons of distributions have found a link to information theory in the literature (see, for instance, Ebrahimi et al [ 39 ], Belzunce et al [ 40 ], Nanda and Prasanta [ 41 ], Qiu [ 42 ], Toomaj and Di Crescenzo [ 43 ] and Toomaj and Di Crescenzo [ 44 ]).…”

Section: Stochastic Orderingsmentioning

confidence: 99%

Stochastic Comparisons of Weighted Distributions and Their Mixtures

Al-Babtain

Shrahili

Alshehri

et al. 2020

Entropy

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In this paper, various stochastic ordering properties of a parametric family of weighted distributions and the associated mixture model are developed. The effect of stochastic variation of the output random variable with respect to the parameter and/or the underlying random variable is specifically investigated. Special weighted distributions are considered to scrutinize the consistency as well as the usefulness of the results. Stochastic comparisons of coherent systems made of identical but dependent components are made and also a result for comparison of Shannon entropies of weighted distributions is developed.

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Section: Stochastic Orderingsmentioning

confidence: 99%

Stochastic Comparisons of Weighted Distributions and Their Mixtures

Al-Babtain

Shrahili

Alshehri

et al. 2020

Entropy

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“…Various bounds on quantile-based entropy in the past lifetime for different aging classes are available in Sunoj et al [22]. Qiu [18] further derived some sufficient conditions based on certain aging classes for quantile-based entropy in past lifetime. Also, Sankaran et al [19] and Sunoj et al [23], respectively, obtained bounds on quantile-based Kullback-Leibler and Renyi's divergence measures in past lifetime.…”

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confidence: 99%

Quantile-Based Study of (Dynamic) Inaccuracy Measures

Kayal¹,

Moharana²,

Sunoj³

2019

Prob. Eng. Inf. Sci.

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In the present communication, we introduce quantile-based (dynamic) inaccuracy measures and study their properties. Such measures provide an alternative approach to evaluate inaccuracy contained in the assumed statistical models. There are several models for which quantile functions are available in tractable form, though their distribution functions are not available in explicit form. In such cases, the traditional distribution function approach fails to compute inaccuracy between two random variables. Various examples are provided for illustration purpose. Some bounds are obtained. Effect of monotone transformations and characterizations are provided.

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“…The quantile version of various entropies was presented with the purposes of providing alternative ways, new results and different methods of stochastic comparisons. For details we refer to Sunoj and Sankaran (2012), Yu and Wang (2013), Nanda et al (2014), Sunoj et al (2017) and Qiu (2019). The quantile function strategy allows us to discover some results which are hard to obtain using the definition of survival and past extropies in the form of the underlying distribution function.…”

mentioning

confidence: 99%