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 (α0,α) where α0 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 S0 = -S1. Here 1 represents an m×1 vector with every element being 1.
Read more about this topic: Phase-type Distribution
Famous quotes containing the word definition:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
—Ana Castillo (b. 1953)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)