On weighted cumulative residual entropy

Mirali, M.; Baratpour, S.; Fakoor, Vahid

doi:10.1080/03610926.2015.1053932

Cited by 47 publications

(37 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is a concept dual to the cumulative residual entropy which relates uncertainty on the future lifetime of the system. Mirali et al (2016) introduced the Weighted Cumulative Residual Entropy (WCRE) of X as Mirali and Baratpour (2017) introduced the Weighted Cumulative Entropy (WCE) of X as…”

Section: Introductionmentioning

confidence: 99%

On Cumulative Entropies in Terms of Moments of Order Statistics

Buono

Longobardi

2021

Methodol Comput Appl Probab

View full text Add to dashboard Cite

In this paper, relations between some kinds of cumulative entropies and moments of order statistics are established. By using some characterizations and the symmetry of a non-negative and absolutely continuous random variable X, lower and upper bounds for entropies are obtained and illustrative examples are given. By the relations with the moments of order statistics, a method is shown to compute an estimate of cumulative entropies and an application to testing whether data are exponentially distributed is outlined.

show abstract

Section: Introductionmentioning

confidence: 99%

On Cumulative Entropies in Terms of Moments of Order Statistics

Buono

Longobardi

2021

Methodol Comput Appl Probab

View full text Add to dashboard Cite

show abstract

“…is the weighted CRE; see Misagh and Yari [23], Kayal and Moharana [18], and Mirali, Baratpour and Fakoor [22]. We point out that the weighted CRE is an extension of the weighted (differential) Shannon entropy, considered by Di Crescenzo and Longobardi [9].…”

Section: A Concluding Remarkmentioning

confidence: 86%

On the Elasticity of Expected Interepoch Intervals in a Non-Homogeneous Poisson Process Under Small Variations of Hazard Rate

Psarrakos

Toomaj

2019

Prob. Eng. Inf. Sci.

View full text Add to dashboard Cite

The elasticity of life expectancy is an important feature in life tables. It is also known as life table entropy in the areas of demography and biology, and as normalized cumulative residual entropy in reliability theory. The elasticity of life expectancy provides useful information on studying the way in which small variations in the force of mortality (or hazard rate) affects the life expectancy. In this paper, a perturbation analysis of the hazard rate to the expected interepoch intervals in a non-homogeneous Poisson process is applied, and further interpretations are given by using a normalized version of the generalized cumulative residual entropy. Properties of the elasticity, including ordering results, bounds and empirical estimation, are obtained. Moreover, the dynamic version of the elasticity is studied, and some monotonicity and characterization results are given.

show abstract

“…Rao et al [ 4 ] introduced cumulative residual entropies as a Shannon entropy, where the density is substituted by the survival function. Then, [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ] discussed this cumulative residual Shannon entropy:

DiCrescenzo and Longobardi [ 41 ] applied the Shannon entropy to a distribution function and called it cumulative entropy. This gave the formula

We will call ( 4 ) cumulative direct Shannon entropy (

) for a better distinction to the cumulative residual Shannon entropy (

) and the cumulative paired Shannon entropy (

).…”

Section: What Does Maximizing Cumulative Direct Residual and Paimentioning

confidence: 99%

“…The exponential and more generally, the Weibull distribution, are solutions to these special ME tasks. In the following years, several authors [ 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ] also focused on cumulative residual entropies. In particular, Drissi et al [ 10 ] were concerned with the ME problem.…”

Section: Introductionmentioning

confidence: 99%

(Generalized) Maximum Cumulative Direct, Residual, and Paired Φ Entropy Approach

Klein

Doll²

2020

Entropy

View full text Add to dashboard Cite

A distribution that maximizes an entropy can be found by applying two different principles. On the one hand, Jaynes (1957a,b) formulated the maximum entropy principle (MaxEnt) as the search for a distribution maximizing a given entropy under some given constraints. On the other hand, Kapur (1994) and Kesavan and Kapur (1989) introduced the generalized maximum entropy principle (GMaxEnt) as the derivation of an entropy for which a given distribution has the maximum entropy property under some given constraints. In this paper, both principles were considered for cumulative entropies. Such entropies depend either on the distribution function (direct), on the survival function (residual) or on both (paired). We incorporate cumulative direct, residual, and paired entropies in one approach called cumulative Φ entropies. Maximizing this entropy without any constraints produces an extremely U-shaped (=bipolar) distribution. Maximizing the cumulative entropy under the constraints of fixed mean and variance tries to transform a distribution in the direction of a bipolar distribution, as far as it is allowed by the constraints. A bipolar distribution represents so-called contradictory information, which is in contrast to minimum or no information. In the literature, to date, only a few maximum entropy distributions for cumulative entropies have been derived. In this paper, we extended the results to well known flexible distributions (like the generalized logistic distribution) and derived some special distributions (like the skewed logistic, the skewed Tukey λ and the extended Burr XII distribution). The generalized maximum entropy principle was applied to the generalized Tukey λ distribution and the Fechner family of skewed distributions. Finally, cumulative entropies were estimated such that the data was drawn from a maximum entropy distribution. This estimator will be applied to the daily S&P500 returns and time durations between mine explosions.

show abstract

On weighted cumulative residual entropy

Cited by 47 publications

References 15 publications

On Cumulative Entropies in Terms of Moments of Order Statistics

On Cumulative Entropies in Terms of Moments of Order Statistics

On the Elasticity of Expected Interepoch Intervals in a Non-Homogeneous Poisson Process Under Small Variations of Hazard Rate

(Generalized) Maximum Cumulative Direct, Residual, and Paired Φ Entropy Approach

Contact Info

Product

Resources

About