IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov processes
In a time-homogeneous continuous-time Markov jump process, the holding time in state i has which distribution, and what is its parameter?
The holding time in state i is exponential with parameter equal to the total transition rate out of i, the sum of all rates to other states, because the Markov property requires a memoryless waiting time.
- AExponential with parameter equal to the sum of the transition rates out of state iCorrect
- BExponential with parameter equal to the rate of a single chosen transition
- CGamma with shape equal to the number of states
- DUniform on (0,1/λ_i) where λ_i is the total exit rate
- Normal with mean equal to 1/λ_i
Explanation
Memorylessness from the Markov property forces exponential holding times. The rate is the total exit rate λ_i = Σ_{j≠i} μ_ij. A single transition's rate gives only the jump-specific intensity, not the holding time.
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