Stochastic orderings of convolution residuals

Stochastic orderings of convolution residuals Article

Amiripour, F, Khaledi, BE, Shaked, M. (2013). Stochastic orderings of convolution residuals . METRIKA, 76(4), 559-576. 10.1007/s00184-012-0404-x

In this paper we study convolution residuals, that is, if X1, X2, ..., Xn are independent random variables, we study the distributions, and the properties, of the sums ∑i=1^l Xi - t given that ∑i=1^k Xi > t, where t ∈ ℝ, and 1 ≤ k ≤ l ≤ n. Various stochastic orders, among convolution residuals based on observations from either one or two samples, are derived. As a consequence computable bounds on the survival functions and on the expected values of convolution residuals are obtained. Some applications in reliability theory and queueing theory are described. © 2012 Springer-Verlag.