Displaying similar documents to “Phase-type distributions and perturbation model”

Some properties of the proportional odds model

Magdalena Benduch-Frąszczak (2010)

Applicationes Mathematicae

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Marshall and Olkin (1997) introduced a new family of distributions by adding a tilt parameter. The same family was obtained by Kirmani and Gupta (2001) as the proportional odds model, which had been proposed by Clayton (1974). In this paper, stochastic ordering of distributions from this class and preservation of classes of life distributions by adding a parameter are obtained. The proportional odds family is also considered as a family of weighted distributions.

The elementary theory of distributions (I)

Jan Mikusiński, Roman Sikorski

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CONTENTS Introduction........................................................................................................... 3 § 1. The abstraction principle............................................................................... 4 § 2. Fundamental sequences of continuous functions......................................... 5 § 3. The definition of distributions........................................................................ 9 § 4. Distributions as a generalization of...

Distributions that are functions

Ricardo Estrada (2010)

Banach Center Publications

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It is well-known that any locally Lebesgue integrable function generates a unique distribution, a so-called regular distribution. It is also well-known that many non-integrable functions can be regularized to give distributions, but in general not in a unique fashion. What is not so well-known is that to many distributions one can associate an ordinary function, the function that assigns the distributional point value of the distribution at each point where the value exists, and that...

Weighting, likelihood ratio order and life distributions

Magdalena Skolimowska, Jarosław Bartoszewicz (2006)

Applicationes Mathematicae

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We use weighted distributions with a weight function being a ratio of two densities to obtain some results of interest concerning life and residual life distributions. Our theorems are corollaries from results of Jain et al. (1989) and Bartoszewicz and Skolimowska (2006).

The elementary theory of distributions (II)

Jan Mikusiński, Roman Sikorski

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CONTENTS Introduction................................................................................... 3 § 1. Terminology and notation.................................................................................... 4 § 2. Uniform and almost uniform convergence....................................................... 6 § 3. Fundamental sequences of smooth functions............................................... 6 § 4. The definition of distributions................................................................................