A quantile-based Tsallis-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml62" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>α</mml:mi></mml:math> divergence

Kayal, Suchandan; Tripathy, Manas Ranjan

doi:10.1016/j.physa.2017.10.023

Cited by 15 publications

(4 citation statements)

References 17 publications

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“…If basically φp0q " φp1q " 0 and P , Q are generated by random variables, say P " P rrX P ¨s, Q " P rrY P ¨s -and thus F P pzq " P rrX ď zs, F Q pzq " P rrY ď zs -then according to (97) the CP D φ pP, Qq coincides with the cumulative paired φ´divergence CP D φ pX, Y q of Klein et al [105]; the special case CP D φα pX, Y q with φ " φ α from ( 26) was employed by Jager & Wellner [91]. Notice that without the assumption φp1q " 0 " φ 1 p1q, the right-hand side of (97) may become negative and thus is not a divergence anymore.…”

Section: Connections With Optimal Transport and Couplingmentioning

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: Connections With Optimal Transport and Couplingmentioning

confidence: 99%

A Unifying Framework for Some Directed Distances in Statistics

Broniatowski¹,

Stummer²

2022

Preprint

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“…Quantile-based information measures have been used by many researchers in the context of information theory. We refer to the reader, Sunoj and Sankaran [35], Sunoj et al [37], Nanda et al [26], Kumar and Rekha [18], Kayal and Tripathy [14] and Krishnan et al [16] and many others.…”

Section: Kumar and N Singhmentioning

confidence: 99%

Some Results on Quantile-based Dynamic Survival and Failure Tsallis Entropy

Kumar¹,

Rani

Singh

2021

Tamkang J. Math.

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Non-additive entropy measures are important for many applications. In this paper, we introduce a quantile-based non-additive entropy measure, based on Tsallis entropy and study their properties. Some relationships of this measure with well-known reliability mea- sures and ageing classes are studied and some characterization results are presented. Also the concept of quantile-based shift independent entropy measures has been introduced and studied various properties.

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“…Also, Sunoj et al [25] studied a quantile-based Tsallis entropy and its order statistics. However, Kayal and Tripathy [8] introduced Tsallis divergence of order α and proved some properties including bounds and effect of transformations. Motivated by these, here, we consider quantile version of inaccuracy and its dynamic forms.…”

Section: )mentioning

confidence: 99%

“…Several authors proved that the Lehman alternative family (or PRHM) is characterized by a constant value of various quantile-based past information measures. For instance, see Sankaran et al [19], Sunoj et al [23] and Kayal and Tripathy [8]. Let X 1 and X 2 satisfy PRHM.…”

Section: )mentioning

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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A quantile-based Tsallis-α divergence

Cited by 15 publications

References 17 publications

A Unifying Framework for Some Directed Distances in Statistics

A Unifying Framework for Some Directed Distances in Statistics

Some Results on Quantile-based Dynamic Survival and Failure Tsallis Entropy

Quantile-Based Study of (Dynamic) Inaccuracy Measures

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