The purpose of this paper is to present a general universal formula for <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;&...The purpose of this paper is to present a general universal formula for <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate survival functions for arbitrary <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2, 3, <span style="font-family:;" "=""><span style="font-family:Verdana;">...<span style="font-family:Verdana;">, given all the univariate marginal survival functions. This universal form of <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><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 style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2 and the main results for the case <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 3 were formulated as Theorem 1 and Theorem 2 in Section 4. Nevertheless, the hypothetical conditions valid for the general <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> ≥ 4 case were also formulated in Section 3 as the (very convincing) Hypothesis. As for the sufficient conditions for both the <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:;" "=""><span style="font-family:Verdana;"> = 3 and <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> ≥ 4 cases, the full generality was not achieved since two restrictions were imposed. Firstly, we limited ourselves to the, defined in the text, “continuous cases” (when the corresponding joint density exists and is continuous), and secondly we consider positive stochastic dependencies only. Nevertheless, the class of the <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate distributions which can be constructed is very wide. The presented method of construction by means of joiners can be considered competitive to the <span style="font-family:Verdana;"><span style="font-family:Verdana;">copula<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> methodology. As it is suggested in the paper the possibility of building a common theory of both copulae and joiners is quite possible, and the joiners may play the role of tools within the theory of copulae, and vice versa copulae may, for example, be used for finding proper joiners. Another independent feature of the joiners methodology is the possibility of constructing many new stochastic processes including stationary and Markovian.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
大家可能收集了许多视频文件，但由于视频文件格式众多，要想将其合并起来会很麻烦。因为一般的软件只能合并同类型的视频文件，对于不同格式的视频文件无法合并，如果非要进行合并就必须先把不同格式的文件全部转换成同一格式后才可以...大家可能收集了许多视频文件，但由于视频文件格式众多，要想将其合并起来会很麻烦。因为一般的软件只能合并同类型的视频文件，对于不同格式的视频文件无法合并，如果非要进行合并就必须先把不同格式的文件全部转换成同一格式后才可以进行，实在是非常麻烦。有了All Video Joiner这款软件就能轻松地解决这个难题，它是个“大肚汉”，可以把多个不同格式的视频文件合并到一个大的视频文件中，包容性极强。例如它可以将几个AVI视频、MPEG视频或者ASF视频合并在一起，方便我们保存和观看。展开更多
文摘The purpose of this paper is to present a general universal formula for <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate survival functions for arbitrary <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2, 3, <span style="font-family:;" "=""><span style="font-family:Verdana;">...<span style="font-family:Verdana;">, given all the univariate marginal survival functions. This universal form of <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><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 style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2 and the main results for the case <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 3 were formulated as Theorem 1 and Theorem 2 in Section 4. Nevertheless, the hypothetical conditions valid for the general <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> ≥ 4 case were also formulated in Section 3 as the (very convincing) Hypothesis. As for the sufficient conditions for both the <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:;" "=""><span style="font-family:Verdana;"> = 3 and <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> ≥ 4 cases, the full generality was not achieved since two restrictions were imposed. Firstly, we limited ourselves to the, defined in the text, “continuous cases” (when the corresponding joint density exists and is continuous), and secondly we consider positive stochastic dependencies only. Nevertheless, the class of the <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate distributions which can be constructed is very wide. The presented method of construction by means of joiners can be considered competitive to the <span style="font-family:Verdana;"><span style="font-family:Verdana;">copula<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> methodology. As it is suggested in the paper the possibility of building a common theory of both copulae and joiners is quite possible, and the joiners may play the role of tools within the theory of copulae, and vice versa copulae may, for example, be used for finding proper joiners. Another independent feature of the joiners methodology is the possibility of constructing many new stochastic processes including stationary and Markovian.
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.
文摘大家可能收集了许多视频文件，但由于视频文件格式众多，要想将其合并起来会很麻烦。因为一般的软件只能合并同类型的视频文件，对于不同格式的视频文件无法合并，如果非要进行合并就必须先把不同格式的文件全部转换成同一格式后才可以进行，实在是非常麻烦。有了All Video Joiner这款软件就能轻松地解决这个难题，它是个“大肚汉”，可以把多个不同格式的视频文件合并到一个大的视频文件中，包容性极强。例如它可以将几个AVI视频、MPEG视频或者ASF视频合并在一起，方便我们保存和观看。
