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Marshall ̶ Olkin Distributions - Advances in Theory and Applications pp 51–64Cite as

General Marshall–Olkin Models, Dependence Orders, and Comparisons of Environmental Processes

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 141))

Abstract

In many applicative fields, the behavior of a process \(\mathbf {Z}\) is assumed to be subjected to an underlying process \(\varTheta \) that describes evolutions of environmental conditions. A common way to define the environmental process is by letting the marginal values of \(\varTheta \) subjected to specific environmental factors (constant along time) and factors describing the conditions of the environment at the specified time. In this paper we describe some recent results that can be used to compare two of such environmental discrete-time processes \(\varTheta \) and \(\widetilde{\varTheta }\) in dependence. A sample of applications of the effects of these comparison results on the corresponding processes \(\mathbf {Z}\) and \(\widetilde{\mathbf {Z}}\) in some different applicative contexts are provided.

We sincerely thank the referee for the careful reading of the paper.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Haifa, Haifa, Israel

    Esther Frostig

  2. Dipartimento di Scienze Matematiche, Politecnico di Torino, Turin, Italy

    Franco Pellerey

Authors
  1. Esther Frostig
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  2. Franco Pellerey
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Corresponding author

Correspondence to Franco Pellerey .

Editor information

Editors and Affiliations

  1. Department of Statistics, University of Bologna, Bologna, Italy

    Umberto Cherubini

  2. Free University of Bozen-Bolzano, Faculty of Economics and Management, Bolzano, Italy

    Fabrizio Durante

  3. University of Bologna, Department of Statistics, Bologna, Italy

    Sabrina Mulinacci

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Frostig, E., Pellerey, F. (2015). General Marshall–Olkin Models, Dependence Orders, and Comparisons of Environmental Processes. In: Cherubini, U., Durante, F., Mulinacci, S. (eds) Marshall ̶ Olkin Distributions - Advances in Theory and Applications. Springer Proceedings in Mathematics & Statistics, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-319-19039-6_4

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