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CONVEX COMPARISONS FOR RANDOM SUMS IN RANDOM ENVIRONMENTS AND APPLICATIONS

Published online by Cambridge University Press:  27 May 2008

José María Fernández-Ponce ,
Eva María Ortega  and
Franco Pellerey
José María Fernández-Ponce
Affiliation:
Departamento Estadística e Investigación Operativa Facultad de MatemáticasUniversidad de Sevilla41012 Sevilla, Spain E-mail: ferpon@us.es
Eva María Ortega
Affiliation:
Centro de Investigación Operativa Escuela Politécnica Superior de OrihuelaUniversidad Miguel Hernández03312 Orihuela (Alicante), Spain E-mail: evamaria@umh.es
Franco Pellerey
Affiliation:
Dipartimento di Matematica Politecnico di Torino c.so Duca Degli Abruzzi 24 10129 Torino, Italy E-mail: franco.pellerey@polito.it
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Abstract

Recently, Belzunce, Ortega, Pellerey, and Ruiz [3] have obtained stochastic comparisons in increasing componentwise convex order sense for vectors of random sums when the summands and number of summands depend on a common random environment, which prove how the dependence among the random environmental parameters influences the variability of vectors of random sums. The main results presented here generalize the results in Belzunce et al. [3] by considering vectors of parameters instead of a couple of parameters and the increasing directionally convex order. Results on stochastic directional convexity of families of random sums under appropriate conditions on the families of summands and number of summands are obtained, which lead to the convex comparisons between random sums mentioned earlier. Different applications in actuarial science, reliability, and population growth are also provided to illustrate the main results.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 3 , July 2008 , pp. 389 - 413
Copyright
Copyright © Cambridge University Press 2008

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