We introduce a multivariate class of distributions with support I, a k-orthotope in $[0,\infty)^{k}$ , which is dense in the set of all k-dimensional distributions with support I. We call this new class ‘multivariate finite-support phase-type distributions’ (MFSPH). Though we generally define MFSPH distributions on any finite k-orthotope in $[0,\infty)^{k}$ , here we mainly deal with MFSPH distributions with support $[0,1)^{k}$ . The distribution function of an MFSPH variate is computed by using that of a variate in the MPH $^{*} $ class, the multivariate class of distributions introduced by Kulkarni (1989). The marginal distributions of MFSPH variates are found as FSPH distributions, the class studied by Ramaswami and Viswanath (2014). Some properties, including the mixture property, of MFSPH distributions are established. Estimates of the parameters of a particular class of bivariate finite-support phase-type distributions are found by using the expectation-maximization algorithm. Simulated samples are used to demonstrate how this class could be used as approximations for bivariate finite-support distributions.

中文翻译：

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多元有限支持相型分布

我们引入了具有支持的多元分布类一世， 一种ķ-原位在$[0,\infty)^{k}$，它在所有的集合中是稠密的ķ有支持的维分布一世. 我们称这个新类为“多元有限支持相型分布”（MFSPH）。虽然我们通常在任何有限的ķ-原位在$[0,\infty)^{k}$, 这里我们主要处理有支持的 MFSPH 分布$[0,1)^{k}$. MFSPH 变量的分布函数是通过使用 MPH 中的变量的分布函数计算的$^{*} $类，由 Kulkarni (1989) 引入的多元分布类。MFSPH 变量的边际分布被发现为 FSPH 分布，Ramaswami 和 Viswanath (2014) 研究的类。建立了 MFSPH 分布的一些性质，包括混合性质。通过使用期望最大化算法找到特定类的二元有限支持相型分布的参数估计。模拟样本用于演示如何将此类用作二元有限支持分布的近似值。