A NEW LOGARITHMIC TYPE ESTIMATORS FOR ANALYSIS OF NUMBER OF AFTERSHOCKS USING POISSON DISTRIBUTION

Earthquake is a fierce and unavoidable natural disaster. The study of aftershocks following an earthquake provides a comprehensive understanding of seismic activity, making it an important area of research. Although it is important to mention that the use of the Poisson distributed population, to estimate the mass mean of rare events such as earthquakes, has been little studied in the literature. In this context, this study proposes a new class of logarithmic type ratio estimators for estimating the mean of a Poisson distributed population in a simple random sampling without replacement. The proposed estimators are obtained using the logarithmic transformation of the ratio estimator, and the expressions for the mean square error (MSE) are also derived to the first order of approximation. The study demonstrates that the proposed logarithmic type estimators are more efficient than the existing estimators, both theoretically and empirically. The Empirical evidence from a real data study conducted using earthquake data from Turkey confirms the superiority of the proposed estimators over the existing estimators. The study provides valuable insights for researchers and practitioners working with Poisson distributed populations and requiring ratio estimators using simple random sampling without replacement.