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## Moment matching algorithms

A moment matching algorithm maps a general probability distribution, , into a PH distribution, . A PH distribution is a combination of exponential distributions with a certain structure. Examples of PH distributions include an exponential distribution, the convolution of exponential distributions, and a mixture of exponential distributions. More formally, a PH distribution is defined as the distribution of the time until absorption in a Markov chain (see Figure 2.1). Thus, essentially, a moment matching algorithm takes a general probability distribution, , as an input, and outputs a Markov chain with an absorbing state together with the probability vector for the initial state, such that some moments of the distribution of the absorption time in the Markov chain (the PH distribution, ) agree with those of . By convention, when the Markov chain has states, we say that the PH distribution has phases.

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Takayuki Osogami 2005-07-19