Bivariate extension of (dynamic) cumulative past entropy

Kundu, Amarjit; Kundu, Chanchal

doi:10.1080/03610926.2015.1080838

Cited by 12 publications

(11 citation statements)

References 29 publications

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“…) is a bivariate random vector with appropriate support. The results presented here generalize and enhance the similar related results of Rajesh et al (2014) and Kundu and Kundu (2017).…”

Section: Proposition 18 Let X and Y Be Two Absolutely Continuous Nonnegative Random Variables Thensupporting

confidence: 91%

“…Even though a lot of interest has been evoked on the study of the aforesaid measures with reference to residual/past lifetime in the univariate case, only few works seem to have been done in higher dimensions. Recently, Rajesh et al (2014) and Kundu and Kundu (2017) have considered extension of DCRE and DCPE, respectively, to bivariate setup and study their properties. Some bivariate distributions have also been characterized there.…”

Section: Proposition 18 Let X and Y Be Two Absolutely Continuous Nonnegative Random Variables Thenmentioning

confidence: 99%

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Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures

Ghosh

Kundu

2017

Stat Papers

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In a recent paper, Kundu et al. (Metrika 79:335-356, 2016) study the notion of cumulative residual inaccuracy (CRI) and cumulative past inaccuracy (CPI) measures in univariate setup as a generalization of cumulative residual entropy and cumulative past entropy, respectively. Here we address the question of extending the definition of CRI (CPI) to bivariate setup and study their properties. We also prolong these measures to conditionally specified models of two components having possibly different ages or failed at different time instants called conditional CRI (CCRI) and conditional CPI (CCPI), respectively. We provide some bounds on using usual stochastic order and investigate several properties of CCRI (CCPI) including the effect of linear transformation. Moreover, we characterize some bivariate distributions. KeywordsCumulative residual (past) inaccuracy • Conditionally specified model • Conditional proportional (reversed) hazard rate • Usual stochastic order

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“…) is a bivariate random vector with appropriate support. The results presented here generalize and enhance the similar related results of Rajesh et al (2014) and Kundu and Kundu (2017).…”

Section: Proposition 18 Let X and Y Be Two Absolutely Continuous Nonnegative Random Variables Thensupporting

confidence: 91%

Section: Proposition 18 Let X and Y Be Two Absolutely Continuous Nonnegative Random Variables Thenmentioning

confidence: 99%

Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures

Ghosh

Kundu

2017

Stat Papers

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“…In the following we have a relationship between CWPE with conditional cumulative past entropy (see Kundu et al (2016)), the bivariate extension of entropy introduced by Di Crescenzo and Longobardi (2009) and is given bȳ…”

Section: Propertiesmentioning

confidence: 99%

Bivariate Weighted Residual and Past Entropies

Rajesh¹,

Abdul-Sathar

Nair

2016

JJSS

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The weighted entropy introduced by Belis and Guiasu (1968) is viewed as a measure of uncertainty. Di Crescenzo and Longobardi (2006) proposed dynamic form of these measure namely weighted residual (WRE) and past entropies (WPE). In this paper, we extend the definition of weighted residual and past entropies to bivariate setup and obtain some of its properties. Several properties, including monotonicity and bounds of BWRE and BWRP are obtained. We also look into the problem of extending WRE and WPE for conditionally specified models. Several properties, including bounds of CWRE and CWPE are obtained for conditional distributions. It is shown that the proposed measure uniquely determines the distribution function.

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“…Several generalizations to the concept of bivariate DCRE can also be found in Sunoj and Linu (2012) and Rajesh et al (2014b). Recently, Kundu and Kundu (2017) have considered the extension of CPE, a dual measure of CRE to bivariate setup and obtained some of its properties. The generalized version of cumulative past entropy can be seen in Kundu and Kundu (2018).…”

Section: Introductionmentioning

confidence: 99%

Bivariate Extension of Past Entropy

Rajesh

Abdul-Sathar

Reshmi

2020

JIRSS

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Di Crescenzo and Longobardi (2002) has been proposed a measure of uncertainty related to past life namely past entropy. The present paper addresses the question of extending this concept to bivariate set-up and study some properties of the proposed measure. It is shown that the proposed measure uniquely determines the distribution function. Characterizations for some bivariate lifetime models are obtained using the proposed measure. Further, we define new classes of life distributions based on this measure and properties of the new classes are also discussed. We also proposed a non-parametric kernel estimator for the proposed measure and illustrated performance of the estimator using a numerical data.

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Bivariate extension of (dynamic) cumulative past entropy

Cited by 12 publications

References 29 publications

Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures

Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures

Bivariate Weighted Residual and Past Entropies

Bivariate Extension of Past Entropy

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