Inference on Parameters of a Geometric Process with Scaled Muth Distribution

Abstract

The problem of statistical modeling of the geometric count data with a specific probability model of lifetimes is of interest and importance in reliability. In this paper, we construct a geometric process (GP), with parameter [Formula: see text], for modeling the geometric count data when the distribution of first occurrence time is a scaled Muth with parameters [Formula: see text] and [Formula: see text]. We investigate the estimators of the process parameters [Formula: see text], [Formula: see text] and [Formula: see text] from a point of approximations of classical and modified approach by using the different estimation methodologies such as the maximum likelihood, moments, least-squares and maximum spacing. We perform a simulation study to compare the estimation performance of the estimators obtained. Finally, we provide an illustrative analysis conducted on a real-world dataset to show the efficiency of the GP model constructed in this paper against the alpha-series and renewal processes and exemplify the data modeling stages. Consequently, a forecasting to such data using the GP with the scaled Muth is investigated.