Prediction of the earthquake magnitudes with A new estimator via sub-sampling method

Türkiye is situated on active fault lines, where significant tectonic movements occur, resulting in earthquakes, and is located in one of the world’s most active earthquake zones, the Alpine-Himalayan seismic belt. We propose an estimator to examine the population mean of the earthquake magnitude using the information of the largest aftershocks among aftershocks via the sub-sampling method under the non-response scheme. The proposed estimator is obtained and the expressions for the bias, mean square error (MSE) and minimum mean square error are also derived to the first order of approximation. We evaluate earthquakes in the Aegean Region of Türkiye between the years 1900 – 2021mbased on different scenarios within the dataset. The results show that the estimation of the population mean is the perfect fit for the real earthquake magnitude population mean via the proposed estimator. By analyzing earthquake data from Türkiye, we successfully highlighted the practical significance and applicability of our proposed estimator in a real-world scenario.