Moment Estimation in a Markov-Dependent Firing Distribution

The probability distribution of a number of Bernoulli trials required to obtain a preassigned number of successes under Markovian dependence arises in the study of certain weapon systems. If the sequences of observations are completely known, the maximum likelihood estimates can be obtained easily for the parameters in the distribution. However, when only partial information is available on the observed sequences, other methods of estimation, such as the method of moments, are employed. This paper obtains moment estimates of the parameters in this distribution and studies some of their properties.