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

Giorgio Pederzoli (1985)

Trabajos de Estadística e Investigación Operativa

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,...

Stochastic comparison of multivariate random sums

Rafał Kulik (2003)

Applicationes Mathematicae

We establish preservation results for the stochastic comparison of multivariate random sums of stationary, not necessarily independent, sequences of nonnegative random variables. We consider convex-type orderings, i.e. convex, coordinatewise convex, upper orthant convex and directionally convex orderings. Our theorems generalize the well-known results for the stochastic ordering of random sums of independent random variables.

Structural breaks in dependent, heteroscedastic, and extremal panel data

Matúš Maciak, Barbora Peštová, Michal Pešta (2018)

Kybernetika

New statistical procedures for a change in means problem within a very general panel data structure are proposed. Unlike classical inference tools used for the changepoint problem in the panel data framework, we allow for mutually dependent panels, unequal variances across the panels, and possibly an extremely short follow up period. Two competitive ratio type test statistics are introduced and their asymptotic properties are derived for a large number of available panels. The proposed tests are...

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