Construction of <i>k</i>-Variate Survival Functions with Emphasis on the Case <i>k</i>= 3

• 作者: Jerzy K. Filus Lidia Z. Filus
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Construction of Multivariate Probability Distributions via Joiners Joiner versus Copula Methodology A Possible Fusion of the Two Construction Methods k -Variate Survival Function Scheme k = 3 Case
• 年，卷（期）: 2020,（7）
• 页码范围: 678-697
• 页数: 20页
• 分类号: O17

摘要

The purpose of this paper is to present a general universal formula for <span style="font-family:Verdana;"><i></i></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;">-variate survival functions for arbitrary </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2, 3, </span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">...</span><span style="font-family:Verdana;">, given all the univariate marginal survival functions. This universal form of </span></span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;">-variate probability distributions was obtained by means of “dependence functions” named “joiners” in the text. These joiners determine all the involved stochastic dependencies between the underlying random variables. However, in order that the presented formula (the form) represents a legitimate survival function, some necessary and sufficient conditions for the joiners had to be found. Basically, finding those conditions is the main task of this paper. This task was successfully performed for the case </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span></i><span style="font-family:Verdana;"></span></span></span></i><span><span><span style="font-family:Verdana;"> = 2 and the main results for the case </span><span style="font-family:Verdana;"><i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">k</span><