Some properties of beta functions and the distribution for the product of independent beta random variables.

Pederzoli, Giorgio. "Some properties of beta functions and the distribution for the product of independent beta random variables.." Trabajos de Estadística e Investigación Operativa 36.1 (1985): 122-128. <http://eudml.org/doc/40766>.

@article{Pederzoli1985,
abstract = {Products of independent beta random variables appear in a large number of problems in multivariate statistical analysis. In this paper we show how a convenient factorial expansion of gamma ratios can be suitably used in deriving the exact density for a product of independent beta random variables. Possible applications of this result for obtaining the exact densities of the likelihood ratio criteria for testing hypotheses in the multinormal case are also pointed out. For the sake of illustration, the exact null density of Wilks'Λ for testing linear hypothesis in the real Gaussian case is derived. Furthermore, it will be shown that this method is applicable also to problems of a more general nature.},
author = {Pederzoli, Giorgio},
journal = {Trabajos de Estadística e Investigación Operativa},
keywords = {Análisis multivariante; Variables aleatorias; Ensayos; Wilks lambda criterion; factorial expansion of gamma ratios; exact density; product of independent beta random variables; likelihood ratio criteria; multinormal; testing linear hypotheses; real Gaussian case},
language = {eng},
number = {1},
pages = {122-128},
title = {Some properties of beta functions and the distribution for the product of independent beta random variables.},
url = {http://eudml.org/doc/40766},
volume = {36},
year = {1985},
}

TY - JOUR
AU - Pederzoli, Giorgio
TI - Some properties of beta functions and the distribution for the product of independent beta random variables.
JO - Trabajos de Estadística e Investigación Operativa
PY - 1985
VL - 36
IS - 1
SP - 122
EP - 128
AB - Products of independent beta random variables appear in a large number of problems in multivariate statistical analysis. In this paper we show how a convenient factorial expansion of gamma ratios can be suitably used in deriving the exact density for a product of independent beta random variables. Possible applications of this result for obtaining the exact densities of the likelihood ratio criteria for testing hypotheses in the multinormal case are also pointed out. For the sake of illustration, the exact null density of Wilks'Λ for testing linear hypothesis in the real Gaussian case is derived. Furthermore, it will be shown that this method is applicable also to problems of a more general nature.
LA - eng
KW - Análisis multivariante; Variables aleatorias; Ensayos; Wilks lambda criterion; factorial expansion of gamma ratios; exact density; product of independent beta random variables; likelihood ratio criteria; multinormal; testing linear hypotheses; real Gaussian case
UR - http://eudml.org/doc/40766
ER -