Estimation of Parameters of Zero-One Processes by Interval Sampling

M. Brown, H. Solomon and M. A. Stephens
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M. Brown: City University of New York, New York, New York
H. Solomon: Stanford University, Stanford, California
M. A. Stephens: McMaster University, Hamilton, Ontario

Operations Research, 1977, vol. 25, issue 3, 493-505

Abstract: 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.

Date: 1977
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