Non-exchangeability of copulas arising from shock models

Exchangeability and regression models

Sir David Cox’s statistical career and his lifelong interest in the theory and application of stochastic processes began with problems in the wool industry. The problem of drafting a strand of wool yarn to near uniform width is not an auspicious starting point, but an impressive array of temporal and spectral methods from stationary time series were brought to bear on the problem in Cox (1949)....

Solving large systems arising from fractional models by preconditioned methods

This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...

New classes of Extereme Shock Models

 In industry or nature, ‎there are systems subjected to a secuence of shocks ocurring randomly in time‎. ‎these shocks are causing aging or failure of system‎. ‎According to the type of shocks‎, ‎shock models divided in two major groups‎, ‎Extreme Shock Models and Cumulative Shock Models‎. ‎In the extreme shock models just impact of last shock named fatal shock would be studied and in the cumul...

Building Measurement Models from Scratch: Graphical Models, Exchangeability Models, and Log-linear Models

Maximal non-exchangeability in dimension d

We give the maximal distance between a copula and itself when the argument is permuted for arbitrary dimension, generalizing a result for dimension two by Nelsen (2007); Klement and Mesiar (2006). Furthermore, we establish a subset of [0, 1] in which this bound might be attained. For each point in this subset we present a copula and a permutation, for which the distance in this point is maximal...