Estimation of scale parameter in gamma population using samples selected by systematic manner

Abstract

The Systematic sampling method has been proven effective in finite population for estimation of the population characteristics. However, its application to an infinite population requires further exploration. This article aims to extend the systematic sampling method to infinite populations and presents several approximation techniques. The performance of each method is evaluated based on different characteristics of the population distribution. Specifically, we focus on important distributions and investigate the case of Gamma distribution here. Three approaches are considered, with the first method showing promising results. This method involves assigning Gamma probabilities to all possible samples, avoiding the need to truncate the infinite population into a finite one. Also, it is seen that estimates are closed to original one if all samples include mode or neighbourhood of mode. The findings of this study shed light on the applicability of systematic sampling for infinite populations and contribute towards the estimation of population characteristics by this kind of work.

Journal of Statistical Research 2025, Vol. 59, No. 2, pp. 305-323