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="...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><展开更多
Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict o...Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.展开更多
文摘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><
文摘Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.
