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Some ideas for comparison of Bellman chains

Laurent Truffet (2003)

Kybernetika

In this paper we are exploiting some similarities between Markov and Bellman processes and we introduce the main concepts of the paper: comparison of performance measures, and monotonicity of Bellman chains. These concepts are used to establish the main result of this paper dealing with comparison of Bellman chains.

Some inequalities related to the Stam inequality

Abram Kagan, Tinghui Yu (2008)

Applications of Mathematics

Zamir showed in 1998 that the Stam classical inequality for the Fisher information (about a location parameter) 1 / I ( X + Y ) 1 / I ( X ) + 1 / I ( Y ) for independent random variables X , Y is a simple corollary of basic properties of the Fisher information (monotonicity, additivity and a reparametrization formula). The idea of his proof works for a special case of a general (not necessarily location) parameter. Stam type inequalities are obtained for the Fisher information in a multivariate observation depending on a univariate location...

Some properties and applications of probability distributions based on MacDonald function

Oldřich Kropáč (1982)

Aplikace matematiky

In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types x n K n ( x ) , x 0 , x n K n ( x x ) , x 𝐑 and x n + 1 K n ( x ) , x 0 are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and useful applications...

Some properties of the proportional odds model

Magdalena Benduch-Frąszczak (2010)

Applicationes Mathematicae

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.

Some Remarks on Functionals with the Tensorization Property

Paweł Wolff (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

We investigate the subadditivity property (also known as the tensorization property) of φ-entropy functionals and their iterations. In particular we show that the only iterated φ-entropies with the tensorization property are iterated variances. This is a complement to the result due to Latała and Oleszkiewicz on characterization of the standard φ-entropies with the tensorization property.

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