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A note on the convolution of inverted-gamma distributions with applications to the Behrens-Fisher distribution.

Francisco Javier Girón, Carmen del Castillo (2001)

RACSAM

La distribución de Behrens-Fisher generalizada se define como convolución de dos distribuciones t de Student y se relaciona con la distribución gamma invertida por medio de un teorema de representación como una mixtura, respecto del parámetro de escala, de distribuciones normales cuando la distribución de mezcla es la convolución de dos distribuciones gamma invertidas. Un resultado importante de este artículo establece que la distribución de Behrens-Fisher con grados de libertad impares es mixtura...

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.

An Approach to Distribution of the Product of Two Normal Variables

Antonio Seijas-Macías, Amílcar Oliveira (2012)

Discussiones Mathematicae Probability and Statistics

The distribution of product of two normally distributed variables come from the first part of the XX Century. First works about this issue were [1] and [2] showed that under certain conditions the product could be considered as a normally distributed. A more recent approach is [3] that studied approximation to density function of the product using three methods: numerical integration, Monte Carlo simulation and analytical approximation to the result using the normal distribution....

Approximate polynomial expansion for joint density

D. Pommeret (2005)

Applicationes Mathematicae

Let (X,Y) be a random vector with joint probability measure σ and with margins μ and ν. Let ( P ₙ ) n ∈ ℕ and ( Q ₙ ) n ∈ ℕ be two bases of complete orthonormal polynomials with respect to μ and ν, respectively. Under integrability conditions we have the following polynomial expansion: σ ( d x , d y ) = ∑ n , k ∈ ℕ ϱ n , k P ₙ ( x ) Q k ( y ) μ ( d x ) ν ( d y ) . In this paper we consider the problem of changing the margin μ into μ̃ in this expansion. That is the case when μ is the true (or estimated) margin and μ̃ is its approximation. It is shown that a new joint probability with new margins...

Bivariate copulas: Transformations, asymmetry and measures of concordance

Sebastian Fuchs, Klaus D. Schmidt (2014)

Kybernetika

The present paper introduces a group of transformations on the collection of all bivariate copulas. This group contains an involution which is particularly useful since it provides (1) a criterion under which a given symmetric copula can be transformed into an asymmetric one and (2) a condition under which for a given copula the value of every measure of concordance is equal to zero. The group also contains a subgroup which is of particular interest since its four elements preserve symmetry, the...

Characterizacion of the bivariate discrete distributions defined by a partial difference equations system.

Ramón Gutiérrez Jáimez, Miguel Angel Fajardo Caldera (1988)

Trabajos de Estadística

Conditions under which the solutions of a partial difference equations system can be probability functions are examined.When the coefficients of the system are polynomials then the partial difference equations system satisfied by generating functions associated to these distributions are easily obtained; they give useful recurrence relations for the moments. Three examples are given as well.

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