General cumulative Kullback–Leibler information

Park, Sangun; Noughabi, Hadi Alizadeh; Kim, Ilmun

doi:10.1080/03610926.2017.1321767

Cited by 13 publications

(8 citation statements)

References 12 publications

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“…al [204], and Mehrali & Asadi [123] for follow-up papers). For the general context of nonnegative, absolutely continuous random variables (and thus Y " X "s0, 8r) with finite expectations and strictly positive cdf, (77) simplifies to the so-called "cumulative (residual) Kullback-Leibler information" of Baratpour & Habibi Rad [19] (see also Park et al [156] for further properties 17 and Park et al [155] for an extension to the whole real line); the latter has been adapted to a dynamic form by Chamany & Baratpour [44] as follows (adapted to our terminolgy): take arbitrarily fixed "instance" t ě 0, Y " X "st, 8r and replace in (77) the survival function S su x pP q :" t1 ´FP pxqu xPÊ by S su,t x pP q :"…”

Section: Sxpqqmentioning

confidence: 99%

A Unifying Framework for Some Directed Distances in Statistics

Broniatowski¹,

Stummer²

2022

Preprint

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Density-based directed distances -particularly known as divergences -between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine learning. Prominent examples are the Kullback-Leibler information distance (relative entropy) which e.g. is closely connected to the omnipresent maximum likelihood estimation method, and Pearson's χ 2 ´distance which e.g. is used for the celebrated chisquare goodness-of-fit test. Another line of statistical inference is built upon distribution-function-based divergences such as e.g. the prominent (weighted versions of) Cramer-von Mises test statistics respectively Anderson-Darling test statistics which are frequently applied for goodness-of-fit investigations; some more recent methods deal with (other kinds of) cumulative paired divergences and closely related concepts. In this paper, we provide a general framework which covers in particular both the abovementioned density-based and distribution-function-based divergence approaches; the dissimilarity of quantiles respectively of other statistical functionals will be included as well. From this framework, we structurally extract numerous classical and also state-of-the-art (including new) procedures. Furthermore, we deduce new concepts of dependence between random variables, as alternatives to the celebrated mutual information. Some variational representations are discussed, too.

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Section: Sxpqqmentioning

confidence: 99%

A Unifying Framework for Some Directed Distances in Statistics

Broniatowski¹,

Stummer²

2022

Preprint

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“…Analogous to CRE, conditional FCRE can be computed using the fractional CRE of empirical data [30][31][32][33].…”

Section: Empirical Fractional Conditional Cumulative Residual Entropymentioning

confidence: 99%

Some Properties of Fractional Cumulative Residual Entropy and Fractional Conditional Cumulative Residual Entropy

Dong

2022

Fractal Fract

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Fractional cumulative residual entropy is a powerful tool for the analysis of complex systems. In this paper, we first provide some properties of fractional cumulative residual entropy (FCRE). Secondly, we generate cumulative residual entropy (CRE) to the case of conditional entropy, named fractional conditional cumulative residual entropy (FCCRE), and introduce some properties. Then, we verify the validity of these properties with randomly generated sequences that follow different distributions. Moreover, we give the definition of empirical fractional conditional accumulative residual entropy and prove that it can be used to approximate FCCRE. Finally, the empirical analysis of the aero-engine gas path data is carried out. The results show that FCRE and FCCRE can effectively capture complex information in the gas path system.

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“…The choice of α depends on whether to put more weight on earlier difference or later difference. Park et al (2018) considered a normal distribution as an example of distribution functions supported on the whole real line, and proposed GOF test statistics based on CRKL, CKL and GCKL α , respectively. Then, They compared their performances with some competing test statistics based on the empirical distribution function, including the Kolmogorov-Smirnov, Cramer von Mises, and Anderson Darling tests.…”

Section: Test Based On Entropy For Fuzzy Datamentioning

confidence: 99%

“…Because CRKL is defined on the nonnegative random variables, so that ∞ 0 F(x)dx can be defined as E(X), its application has been limited to the semi-infinite intervals. Park et al (2018) extend the application of CRKL to the whole real line as…”

Section: Tests Based On Cumulative Residual Entropy (Cre)mentioning

confidence: 99%

An Updated Review of Goodness of Fit Tests Based on Entropy

Noughabi

Borzadaran

2020

JIRSS

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Different approaches to goodness of fit (GOF) testing are proposed. This survey intends to present the developments on Goodness of Fit based on entropy during the last 50 years, from the very first origins until the most recent advances for different data and models. Goodness of fit tests based on Shannon entropy was started by Vasicek in 1976 and were continued by many authors. In this paper, we describe different GOF tests constructed by authors from the beginning to now. First, the problem of GOF and different types of GOF are stated. Then, the method of GOF tests based on entropy for complete and censored data is explained and all works proposed by authors in this subject are mentioned.

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General cumulative Kullback–Leibler information

Cited by 13 publications

References 12 publications

A Unifying Framework for Some Directed Distances in Statistics

A Unifying Framework for Some Directed Distances in Statistics

Some Properties of Fractional Cumulative Residual Entropy and Fractional Conditional Cumulative Residual Entropy

An Updated Review of Goodness of Fit Tests Based on Entropy

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