represents the distribution of times for the Markov process mproc to pass from the initial state to final states f for the first time.
- FirstPassageTimeDistribution is also known as first hitting time.
- The Markov process mproc can be a DiscreteMarkovProcess or ContinuousMarkovProcess.
- The probability for time t in a FirstPassageTimeDistribution is equivalent to Probability[x[t]∈f∧∀τ,0<τ<tx[τ]∉fxi,xmproc], where i is the initial state.
- If mproc is already in the target state, FirstPassageTimeDistribution gives a distribution for the mean recurrence time.
- If the chain is absorbing and the target states are non-absorbing, FirstPassageTimeDistribution gives a distribution conditional on reaching the target states.
- FirstPassageTimeDistribution represents a discrete phase-type distribution for discrete-time Markov processes and a continuous phase-type distribution for continuous-time Markov processes.
- FirstPassageTimeDistribution can be used with such functions as Mean, Quantile, PDF, and RandomVariate.
Introduced in 2012