Discrete averaged mixing applied to the logarithmic distributions

Author:

Wimmer Gejza1,Mačutek Ján2,Altmann Gabriel3

Affiliation:

1. Mathematical Institute Slovak Academy of Sciences Štefánikova 49 SK–814 73 Bratislava SLOVAKIA Department of Mathematics Faculty of Natural Sciences Matej Bel University SK–947 01 Banská Bystrica SLOVAKIA

2. Department of Applied Mathematics and Statistics Comenius University Mlynská Dolina SK–842 48 Bratislava SLOVAKIA

3. Stüttinghauser Ringstrasse 44 DE–58515 Lüdenscheid GERMANY

Abstract

Abstract A new type of mixtures of discrete probability distributions is presented. A family of discrete averaged mixed distributions is introduced. Its subclass of averaged mixed logarithmic distributions is analyzed. Probabilistic characterizations and connections with other types of mixing are derived. We show also some examples of the analyzed distributions found in literature.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

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2. Cane, V.: Mathematical models for neural networks. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 4, Math. Sci. Publ., Berkeley, CA, 1967, pp. 21–26.

3. Elderton, W. P.—Johnson, N. L.: Systems of Frequency Curves, Cambridge University Press, Cambridge, 2008.

4. Gross, D.—Harris, C. M.: Fundamentals of Queueing Theory, Wiley, New York, 1985.

5. Holgate, P.: A modified geometric distribution arising in trapping studies, Acta Theriologica 9 (1964), 353–356.

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