Showing papers by "Steven E. Rigdon published in 1990"

The effect of assuming a homogeneous poisson process when the true process is a power law process

Abstract: The homogeneous Poisson is the simplest model for describing the random occurrences of events in time, such as the failure times of a repairable system. A more complex model, which includes the homogeneous Poisson process as a special case, is the power..

Estimating the intensity function of a power law process at the current time: time truncated case

Abstract: The power law process, a nonhomogeneous Poisson process with intensity function µ(t) = (β/θ)(t/θ) , is frequently used to model the occurence of events in time Often, an important quantity is the value of the intensity function at the current time, that is, the time when data collection is ceased In this article, the problem of estimating this quantity is addressed when the data are time truncated, that is, when data collection is stopped at a predetermined time T The class of multiples of the conditional MLE is suggested, and some members are analyzed In addition, the class of estimators formed by first performing a preliminary test of significance on the parameter β is analyzed Expressions for the bias and MSE of these estimators are derived and evaluated for several values of the parameters