Estimation of Parameters of Zero-One Processes by Interval Sampling

We consider an alternating renewal process {X(t), t ≧ 0} with states 0 and 1. The periods in state 0 are exponentially distributed with parameter λ, and those in state 1 are exponential with parameter μ. The process is available for sampling only at time epochs that are multiples of a fixed number ▵. The object is to estimate λ and μ from the data. We consider estimation procedures for each of the following sets of data: (i) X(0), X(▵), …, X(n▵), where n is a fixed number of observations; (ii) X(0), X(▵), …, X(M▵), where M is the random number of observations required to have n complete 0-1 cycles.