Recurrence Relations for Moments of Dual Generalized Order Statistics from Weibull Gamma Distribution and Its Characterizations
In this paper, we establish explicit forms and new recurrence relations satisfied by the single and product moments of dua l generalized order statistics from Weibull gamma distribution (WGD). The results include as particular cases the relations for moments of reversed order statistics and lower records. We present characterizations of WGD based on (i) recurrence relation for single moments, (ii) truncated moments of certain function of the variable and (iii) hazrad function.
Expectation identities of lower generalized order statistics from generalized exponential distribution and a characterization
In this paper, we study the explicit expressions and some recurrence relations for single and product moments of lower generalized order statistics from generalized exponential distribution. The results include as particular cases the above relations for moments of order statistics and lower records. Further, using a recurrence relation for single moments we obtain a characterization of generalized exponential distribution.
Graphs of polyhedra; polyhedra as graphs
Relations between graph theory and polyhedra are presented in two contexts. In the first, the symbiotic dependence between 3-connected planar graphs and convex polyhedra is described in detail. In the second, a theory of nonconvex polyhedra is based on a graph-theoretic foundation. This approach eliminates the vagueness and inconsistency that pervade much of the literature dealing with polyhedra more general than the convex ones.