ABSTRACTThe problem of estimating steady state absorption probabilities for first order stationary Markov chains having a finite state space is examined. As model parameters, these probabilities are analytic functions of transition probabilitiesQandR, and they can be represented asP= (I‐Q)‐1R. EstimatorsP̌may be obtained by replacing the transition probabilities by their maximum likelihood estimatorsQandŘunder multinomial theory. Using large sample multivariate normal theory, one can derive the asymptotic distribution of these estimators and can obtain large sample confidence intervals. Finally, an application related to estimating loss reserves for an installment loan portfolio assumed to satisfy a Markov chain is discu