Moments of Truncated Skew-t Distribution and Graph Theory Applied to the Shortest Path Problem

Abstract

In the shortest path problem most approaches has been proposed over the last twenty years are focused to deterministic approaches. Stochastic approaches that include theory of truncated asymmetric probability distributions have not been tackled in the literature of optimal paths. Since, in practice, the paths are distances that must be traveled in finite times which are not always fixed, the stochasticity of the time has to be considered into the problem. In this paper, we consider using the moments of the truncated skew-t distribution to the problem of finding the shortest path between two locations with minimum distance by the transition times. The skew-tand truncated skew-t distributions are described explicitly to show the moments and their existence by the convergence of the hypergeometric series. An application to optimal paths using the moments of the truncated skew-t distribution and the graph theory illustrates the shortest path by the minimum average transition time.