Displaying similar documents to “Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification”

An integral formula for entropy of doubly stochastic operators

Bartosz Frej, Paulina Frej (2011)

Fundamenta Mathematicae

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A new formula for entropy of doubly stochastic operators is presented. It is also checked that this formula fulfills the axioms of the axiomatic definition of operator entropy, introduced in an earlier paper of Downarowicz and Frej. As an application of the formula the 'product rule' is obtained, i.e. it is shown that the entropy of a product is the sum of the entropies of the factors. Finally, the proof of continuity of the new 'static' entropy as a function of the measure is given. ...

Canonical distributions and phase transitions

K.B. Athreya, J.D.H. Smith (2000)

Discussiones Mathematicae Probability and Statistics

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Entropy maximization subject to known expected values is extended to the case where the random variables involved may take on positive infinite values. As a result, an arbitrary probability distribution on a finite set may be realized as a canonical distribution. The Rényi entropy of the distribution arises as a natural by-product of this realization. Starting with the uniform distributionon a proper subset of a set, the canonical distribution of equilibriumstatistical mechanics may...

Further results on the generalized cumulative entropy

Antonio Di Crescenzo, Abdolsaeed Toomaj (2017)

Kybernetika

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Recently, a new concept of entropy called generalized cumulative entropy of order n was introduced and studied in the literature. It is related to the lower record values of a sequence of independent and identically distributed random variables and with the concept of reversed relevation transform. In this paper, we provide some further results for the generalized cumulative entropy such as stochastic orders, bounds and characterization results. Moreover, some characterization results...

On the properties of the Generalized Normal Distribution

Thomas L. Toulias, Christos P. Kitsos (2014)

Discussiones Mathematicae Probability and Statistics

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The target of this paper is to provide a critical review and to enlarge the theory related to the Generalized Normal Distributions (GND). This three term (position, scale shape) distribution is based in a strong theoretical background due to Logarithm Sobolev Inequalities. Moreover, the GND is the appropriate one to support the Generalized entropy type Fisher's information measure.

Maličky-Riečan's entropy as a version of operator entropy

Bartosz Frej (2006)

Fundamenta Mathematicae

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The paper deals with the notion of entropy for doubly stochastic operators. It is shown that the entropy defined by Maličky and Riečan in [MR] is equal to the operator entropy proposed in [DF]. Moreover, some continuity properties of the [MR] entropy are established.

A new approach to mutual information

Fumio Hiai, Dénes Petz (2007)

Banach Center Publications

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A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.