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General proportional mean residual life model

Mohamed Kayid, Salman Izadkhah, Dalal ALmufarrej (2016)

Applications of Mathematics

By considering a covariate random variable in the ordinary proportional mean residual life (PMRL) model, we introduce and study a general model, taking more situations into account with respect to the ordinary PMRL model. We investigate how stochastic structures of the proposed model are affected by the stochastic properties of the baseline and the mixing variables in the model. Several characterizations and preservation properties of the new model under different stochastic orders and aging classes...

Geometric infinite divisibility, stability, and self-similarity: an overview

Tomasz J. Kozubowski (2010)

Banach Center Publications

The concepts of geometric infinite divisibility and stability extend the classical properties of infinite divisibility and stability to geometric convolutions. In this setting, a random variable X is geometrically infinitely divisible if it can be expressed as a random sum of N p components for each p ∈ (0,1), where N p is a geometric random variable with mean 1/p, independent of the components. If the components have the same distribution as that of a rescaled X, then X is (strictly) geometric stable....

Global approximations for the γ-order Lognormal distribution

Thomas L. Toulias (2013)

Discussiones Mathematicae Probability and Statistics

A generalized form of the usual Lognormal distribution, denoted with γ , is introduced through the γ-order Normal distribution γ , with its p.d.f. defined into (0,+∞). The study of the c.d.f. of γ is focused on a heuristic method that provides global approximations with two anchor points, at zero and at infinity. Also evaluations are provided while certain bounds are obtained.

Goodness of fit tests with weights in the classes based on ( h , φ ) -divergences

Elena Landaburu, Leandro Pardo (2000)

Kybernetika

The aim of the paper is to present a test of goodness of fit with weigths in the classes based on weighted h , φ -divergences. This family of divergences generalizes in some sense the previous weighted divergences studied by Frank et al [frank] and Kapur [kapur]. The weighted h , φ -divergence between an empirical distribution and a fixed distribution is here investigated for large simple random samples, and the asymptotic distributions are shown to be either normal or equal to the distribution of a linear...

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