Phase distribution

The phase distribution is a probability distribution that results from convolution or mixing of exponential distributions .

definition

A Markov process with states is given, where the states are transient and the state 0 is absorbing. Every transient state of the Markov process is interpreted as a phase. ${\ displaystyle m + 1 \ geq 2}$ ${\ displaystyle 1, \ ldots, m}$

The continuous phase distribution is then the distribution of the time until the process enters the absorbing state.

The discrete phase distribution is defined analogously, but using a Markov chain .

Special cases

Exponential distribution: a phase.
Erlang distribution : two or more identical phases in a fixed order.

Individual evidence

↑ MF Neut. Matrix-Geometric Solutions in Stochastic Models: an Algorithmic Approach, Chapter 2: Probability Distributions of Phase Type; Dover Publications Inc., 1981

[1] MF Neut. Matrix-Geometric Solutions in Stochastic Models: an Algorithmic Approach, Chapter 2: Probability Distributions of Phase Type; Dover Publications Inc., 1981