In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.

An improved Ritt-Wu’s decomposition (of an algebraic set into the union of irreducible varieties) algorithm is given. The algorithm has been used to prove geometric theorems that Wu’s original method addresses. Unlike Wu’s original approach, nondegenerate conditions are given explicitly at the beginning, not generated during the proof process. A program based on this improved version of the alg...

A classical theorem by Ritt states that all the complete decomposition chains of a univariate polynomial satisfying a certain tameness condition have the same length. In this paper we present our conclusions about the generalization of these theorem in the case of finite coefficient fields when the tameness condition is dropped. (Updated April 2008: see note at the beginning of the introduction.)

in this paper, we derive the exact analytical expressions for the shannon entropy of generalized orderstatistics from pareto-type and related distributions.

in this paper, we obtain  bayesian prediction intervals as well as bayes predictive estimatorsunder square error loss for generalized order statistics when the distribution of the underlying population belongs to a family which includes several important distributions.