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A new weighted Gompertz distribution with applications to reliability data

Hassan S. Bakouch, Ahmed M. T. Abd El-Bar (2017)

Applications of Mathematics

A new weighted version of the Gompertz distribution is introduced. It is noted that the model represents a mixture of classical Gompertz and second upper record value of Gompertz densities, and using a certain transformation it gives a new version of the two-parameter Lindley distribution. The model can be also regarded as a dual member of the log-Lindley- X family. Various properties of the model are obtained, including hazard rate function, moments, moment generating function, quantile function,...

A note on the interval-valued marginal problem and its maximum entropy solution

Jiřina Vejnarová (1998)


This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entropy representatives of these convex sets, are presented. Two counterexamples illustrate the fact, that this property is not generally satisfied. Some ideas of an alternative approach are presented at the end of the paper.

A probability density function estimation using F-transform

Michal Holčapek, Tomaš Tichý (2010)


The aim of this paper is to propose a new approach to probability density function (PDF) estimation which is based on the fuzzy transform (F-transform) introduced by Perfilieva in [10]. Firstly, a smoothing filter based on the combination of the discrete direct and continuous inverse F-transform is introduced and some of the basic properties are investigated. Next, an alternative approach to PDF estimation based on the proposed smoothing filter is established and compared with the most used method...

Asymptotically optimal quantization schemes for Gaussian processes on Hilbert spaces*

Harald Luschgy, Gilles Pagès, Benedikt Wilbertz (2010)

ESAIM: Probability and Statistics

We describe quantization designs which lead to asymptotically and order optimal functional quantizers for Gaussian processes in a Hilbert space setting. Regular variation of the eigenvalues of the covariance operator plays a crucial role to achieve these rates. For the development of a constructive quantization scheme we rely on the knowledge of the eigenvectors of the covariance operator in order to transform the problem into a finite dimensional quantization problem of normal distributions. ...

Compositional models, Bayesian models and recursive factorization models

Francesco M. Malvestuto (2016)


Compositional models are used to construct probability distributions from lower-order probability distributions. On the other hand, Bayesian models are used to represent probability distributions that factorize according to acyclic digraphs. We introduce a class of models, called recursive factorization models, to represent probability distributions that recursively factorize according to sequences of sets of variables, and prove that they have the same representation power as both compositional...

Convex orderings for stochastic processes

Bruno Bassan, Marco Scarsini (1991)

Commentationes Mathematicae Universitatis Carolinae

We consider partial orderings for stochastic processes induced by expectations of convex or increasing convex (concave or increasing concave) functionals. We prove that these orderings are implied by the analogous finite dimensional orderings.

Distribuciones neutras, propensas y resistentes a datos atípicos.

Paloma Main Yaque (1987)

Trabajos de Estadística

Se analizan los conceptos de función de distribución propensa, neutra y resistente a producir datos atípicos dependiendo del comportamiento asintótico de la diferencia y la razón de los dos extremos superiores.Posteriormente se caracterizan las primeras definiciones con propiedades de la cola derecha de la función de distribución.

Equivalence of compositional expressions and independence relations in compositional models

Francesco M. Malvestuto (2014)


We generalize Jiroušek’s (right) composition operator in such a way that it can be applied to distribution functions with values in a “semifield“, and introduce (parenthesized) compositional expressions, which in some sense generalize Jiroušek’s “generating sequences” of compositional models. We say that two compositional expressions are equivalent if their evaluations always produce the same results whenever they are defined. Our first result is that a set system is star-like with centre X if...

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