On Mieshalkin-Rogozin theorem and some decompositions

• Autorzy: Krysicki, W.
• Języki publikacji: EN

Abstrakty

EN

This paper was inspired by the work by A. Chaturredi, U. Rani, Estimation Procedures for a Family of Density Functions Representing Various Life Testing Models, Metrika, Vol. 46 (9), 1997 (formula (1) of this paper), which included a discussion of the four parametric density family. In this paper I discuss possibilities of decompositions of this family and applications of the Mieshalkin-Rogozin theorem.[…] After proving the convergence of the series [formula] (Theorem 2) to lnX with probability one, we represente the function (1) as a density of an infinite product of independent r.v.'s (2 cases). A similar representation of a r.v. gamma type in the form of an infinite product of r.v.'s with the same distribution was used by Lu and Richards [10] to define the square of the Vandermonde determinant with random elements. Finally, we apply the modified Mieshalkin-Rogozin theorem [14] for an estimation of the difference of some distribution functions (see Theorems 7 and 8).

Słowa kluczowe

EN

distribution

• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2000
• Tom: [Z] 40
• Strony: 127-138
• Opis fizyczny: bibliogr. 19 poz.

Twórcy

autor

Krysicki, W.

• Institute of mathematics Technical University of Łódź Al. Politechniki 11 90-924 Łódź, Poland