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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...

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