On stochastic comparison between aggregate claim amounts Article

Khaledi, BE, Saeed Ahmadi, S. (2008). On stochastic comparison between aggregate claim amounts . Journal of Statistical Planning and Inference, 138(7), 2243-2251. 10.1016/j.jspi.2007.10.018

cited authors

  • Khaledi, BE; Saeed Ahmadi, S

abstract

  • Let Xλ1, ..., Xλn be nonnegative independent random variables with Xλi having survival function over(F, -) (., λi), i = 1, ..., n, where λi > 0. Let Ip1, ..., Ipn be independent Bernoulli random variables independent of Xλi with E (Ipi) = pi, i = 1, ..., n. Further, assume that over(F, -) (., λi) is a decreasing and convex function with respect to λi, i = 1, ..., n and that the survival function of ∑i = 1n Xλi is Schur-convex in λ = (λ1, ..., λn). In this paper we show that under the above settings the survival function of S (λ, p) = ∑i = 1n Ipi Xλi is Schur-convex in (λ1, g (p1)), ..., (λn, g (pn)) with respect to multivariate chain majorization, where g (p) = - log p or g (p) = (1 - p) / p and p = (p1, ..., pn). We show an application of the main result in the case that the variables Xλi, i = 1, ..., n, have Weibull or gamma distributions. © 2007 Elsevier B.V. All rights reserved.

authors

publication date

  • July 1, 2008

published in

Digital Object Identifier (DOI)

start page

  • 2243

end page

  • 2251

volume

  • 138

issue

  • 7