Distributions with known initial hazard rate functions

Abstract : The purpose of this paper is to study the distributional properties of a non-negative random vector Image , based on the knowledge of the initial hazard rate functions only. First we study various stochastic orders and stochastic bounds of random vectors that have the same initial hazard rate functions. Then we include some comments about extensions of the results of the paper to n-dimensional vectors (n>2). The results in this paper have various applications in the competing risks theory.