Generalized estimators using characteristics of Poisson distribution

TL;DR

This paper introduces a new class of generalized estimators for estimating the population mean in Poisson-distributed data, demonstrating their superior efficiency through theoretical analysis and empirical validation.

Contribution

It proposes novel exponential estimators based on existing methods, showing they outperform traditional estimators in efficiency for Poisson populations.

Findings

The adapted Solanki and Singh estimator is more efficient than traditional estimators.

The exponential class of estimators is as efficient as the simple difference estimator.

The new estimators outperform existing methods in empirical earthquake data analysis.

Abstract

In this article, we have proposed a generalized class of estimators, exponential class of estimators based on adaption of Sharma and Singh (2015) and Solanki and Singh (2013) and simple difference estimator for estimating unknown population mean in case of Poisson distributed population in simple random sampling without replacement. The expressions for mean square errors of the proposed classes of estimators are derived to the first order of approximation. It is shown that the adapted version of Solanki and Singh (2013), exponential class of estimator, is always more efficient than usual estimator, ratio, product, exponential ratio and exponential product type estimators and equal efficient to simple difference estimator. Moreover, the adapted version of Sharma and Singh (2015) estimator are always more efficient than all the estimators available in literature. In addition, theoretical findings are supported by an empirical study to show the superiority of the constructed estimators over others with earthquake data of Turkey.