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In this article, we have proposed a generalized class of estimators, exponential class of estimators based on adaption of Sharma and Singh (Hacet J Math Stat 44(2):443–453, 2015) and Solanki and Singh (Chil J Stat 4(1):3–17, 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 (Chil J Stat 4(1):3–17, 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 (Hacet J Math Stat 44(2):443–453, 2015) estimator are always more efficient than all the estimators available in literature using characteristics of Poisson distribution. 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.

Generalized Estimators Using Characteristics of Poisson Distribution