Por Mustafa Hilmi Pekalp (Department of Statistics, Faculty of Science, Ankara University).

In this study, we deal with the problem of estimating the mean value and second moment functions in a stochastic monotone process with exponential interarrival times. The unbiasedness, asymptotic unbiasedness and consistency properties of the parametric estimators are investigated. Further, a method for the computation of these estimators is considered depending on the integral equations given for the mean value and second moment functions. The performance of the estimators is evaluated for small sample sizes and different parameter values by a simulation study.