A more general definition of MTP2 (multivariate total positivity of order 2) probability measure is given, without assuming the existence of a density. Under this definition the class of MTP2measures is proved to be closed under weak convergence. Characterizations of the MTP2 property are proved under this more general definition. Then a precise definition of conditionally increasing measure is provided, and closure under weak convergence of the class of conditionally increasing measures is proved. As an application we investigate MTP2properties of stationary distributions of Markov chains, which are of interest in actuarial science.

Positive dependence and weak convergence / Colangelo, A.; Mueller, A.; Scarsini, Marco. - In: JOURNAL OF APPLIED PROBABILITY. - ISSN 0021-9002. - 43:(2006), pp. 48-59. [10.1239/jap/1143936242]

Positive dependence and weak convergence

SCARSINI, MARCO
2006

Abstract

A more general definition of MTP2 (multivariate total positivity of order 2) probability measure is given, without assuming the existence of a density. Under this definition the class of MTP2measures is proved to be closed under weak convergence. Characterizations of the MTP2 property are proved under this more general definition. Then a precise definition of conditionally increasing measure is provided, and closure under weak convergence of the class of conditionally increasing measures is proved. As an application we investigate MTP2properties of stationary distributions of Markov chains, which are of interest in actuarial science.
Positive dependence and weak convergence / Colangelo, A.; Mueller, A.; Scarsini, Marco. - In: JOURNAL OF APPLIED PROBABILITY. - ISSN 0021-9002. - 43:(2006), pp. 48-59. [10.1239/jap/1143936242]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/3153
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