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A phase-type distribution is a probability distribution constructed by a convolution or mixture of exponential distributions. It results from a system of one or more inter-related Poisson processes occurring in sequence, or phases. The sequence in which each of the phases occur may itself be a stochastic process. The distribution can be represented by a random variable describing the time until absorption of a Markov process with one absorbing state. Each of the states of the Markov process represents one of the phases. It has a discrete time equivalent the discrete phase-type distribution. The set of phase-type distributions is dense in the field of all positive-valued distributions, that is, it can be used to approximate any positive-valued distribution. ==Definition== Consider a continuous-time Markov process with ''m'' + 1 states, where ''m'' ≥ 1, such that the states 1,...,''m'' are transient states and state 0 is an absorbing state. Further, let the process have an initial probability of starting in any of the ''m'' + 1 phases given by the probability vector (''α''0,α) where ''α''0 is a scalar and α is a 1 × ''m'' vector. The continuous phase-type distribution is the distribution of time from the above process's starting until absorption in the absorbing state. This process can be written in the form of a transition rate matrix, : where ''S'' is an ''m'' × ''m'' matrix and ''S''0 = –S1. Here 1 represents an ''m'' × 1 vector with every element being 1. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Phase-type distribution」の詳細全文を読む スポンサード リンク
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