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A probability density function estimation using F-transform

Michal Holčapek, Tomaš Tichý (2010)

Kybernetika

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...

A recursion formula for the moments of the gaussian orthogonal ensemble

M. Ledoux (2009)

Annales de l'I.H.P. Probabilités et statistiques

We present an analogue of the Harer–Zagier recursion formula for the moments of the gaussian Orthogonal Ensemble in the form of a five term recurrence equation. The proof is based on simple gaussian integration by parts and differential equations on Laplace transforms. A similar recursion formula holds for the gaussian Symplectic Ensemble. As in the complex case, the result is interpreted as a recursion formula for the number of 1-vertex maps in locally orientable surfaces with a given number of...

A remark on associative copulas

Piotr Mikusiński, Michael D. Taylor (1999)

Commentationes Mathematicae Universitatis Carolinae

A method for producing associative copulas from a binary operation and a convex function on an interval is described.

A second-order stochastic dominance portfolio efficiency measure

Miloš Kopa, Petr Chovanec (2008)

Kybernetika

In this paper, we introduce a new linear programming second-order stochastic dominance (SSD) portfolio efficiency test for portfolios with scenario approach for distribution of outcomes and a new SSD portfolio inefficiency measure. The test utilizes the relationship between CVaR and dual second-order stochastic dominance, and contrary to tests in Post [Post] and Kuosmanen [Kuosmanen], our test detects a dominating portfolio which is SSD efficient. We derive also a necessary condition for SSD efficiency...

A simple proof of Fishburn's moments theorem.

María Lina Martínez García (1985)

Trabajos de Estadística e Investigación Operativa

We derive a necessary condition for stochastic dominance of any order based on the Laplace transform of probability measures on [0,∞) for which it follows easily Fishburn's theorem on the lexicographic order of the moments.

A stochastic fixed point equation for weighted minima and maxima

Gerold Alsmeyer, Uwe Rösler (2008)

Annales de l'I.H.P. Probabilités et statistiques

Given any finite or countable collection of real numbers Tj, j∈J, we find all solutions Fto the stochastic fixed point equation W = d inf j ∈ J T j W j , whereW and the Wj, j∈J, are independent real-valued random variables with distribution Fand = d means equality in distribution. The bulk of the necessary analysis is spent on the case when |J|≥2 and all Tj are (strictly) positive. Nontrivial solutions are then concentrated on either the positive or negative half line. In the most interesting (and difficult) situation T...

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