Recursive formulas for aggregate claim distributions
Relations for the marginal, joint, conditional characteristic functions of k-th upper and lower record values from generalized Pareto distribution and inverse generalized Pareto distribution are given.
In this paper we analyze the construction of -copulas including the ideas of Cuculescu and Theodorescu [5], Fredricks et al. [15], Mikusiński and Taylor [25] and Trutschnig and Fernández-Sánchez [33]. Some of these methods use iterative procedures to construct copulas with fractal supports. The main part of this paper is given in Section 3, where we introduce the sample -copula of order with , the central idea is to use the above methodologies to construct a new copula based on a sample. The...
We say that a random variable X taking nonnegative integers has selective lack-of-memory (SLM) property with selector s if P(X ≥ n + s/X ≥ n) = P(X ≥ s) for n = 0,1,.... This property is characterized in an elementary manner by probabilities pₙ = P(X=n). An application in car insurance is presented.
Copulas are functions which join the margins to produce a joint distribution function. A special class of copulas called shuffles of Min is shown to be dense in the collection of all copulas. Each shuffle of Min is interpreted probabilistically. Using the above-mentioned results, it is proved that the joint distribution of any two continuously distributed random variables X and Y can be approximated uniformly, arbitrarily closely by the joint distribution of another pair X* and Y* each of which...
Let denote the failure rate function of the . and let denote the failure rate function of the mean residual life distribution. In this paper we characterize the distribution functions for which and we estimate when it is only known that or is bounded.