Estimation of Population Mean in an Infinite Population Using Samples by a Systematic Manner

Abstract

Systematic sampling method has been used in a finite population for estimation of the population characteristic. In this article, we are trying to extend this method when the population size is countably infinite. In finite population, a unit has equal probability of being chosen in most of the cases except PPS. However, this cannot be so in infinite population. In that case,we approximate infinite population by large finite population and then use the traditional finite population method. It is true that the original population have some distribution, but without knowing that we are using systematic sampling method and based on that we are estimating population mean. We want to see the effectiveness of this systematic manner if the population has some specified distribution. Here, based on Poisson assumption, we provide some approximation methods and see performances in each case. However, this is to be done for some important distributions also. Here, the problem has been viewed in three ways and out of that the first method performs well, where the Poisson probabilities has been assigned to all possible samples rather than any truncation of the infinite population by finite population. . KEYWORDS :Systematic sampling, Risk function, Poisson distribution, Truncation, Approximation methods.