Self-Switching and Threshold-Driven Lindley Distributions: Applications to Seismicity in North Occidental Algeria (1790–2016)

Abstract

In this paper, we will try to propose a new redistribution to the Lindley distribution in term of threshold dependent modified Lindley distribution (T-RMLD), as a new extension to fit the heterogeneous data sets by the threshold-based method. As such, T-RMLD uses a rate parameter to incorporate varying risk rates and also a threshold mechanism whose purpose is to divide the data into a variety of distinct regions, where each region is under the logical control of a different set of parameters. This allows the model to stay current with the many interacting, changing and heterogeneous patterns seen in real world studies [7-9]. After that, the proposed model was applied to seismic activity data in Northwestern Algeria (1790- 2016) time period, which contains low- and high-magnitude seismic events with distinctive statistical properties that can be appropriate for the study we are trying to conduct. Parameter fitting by maximum likelihood estimation, goodness-of-fit tests for model validation, and comparison with existing Lindley-based distributions are the main methodologies used [10][11]. In the second part of the dissertation, the performance of T-RMLD is compared with that of the benchmark models, employing Monte Carlo simulations that were conducted to assess the goodness of fit measures including the chi-square statistics and the K-S tests. Tests on our data confirmed that such ability from T-RMLD will further improve the accuracy of statistical models for seismic analysis and in turn increase the flexibility and accuracy of the derived results, improve the narrative and analytic tools for describing seismic behavior, and enhance risk assessment frameworks used in major bridge projects. The proposed model extends beyond earthquakes and can be applied to fields where heterogeneous data and variable behavior exist including reliability engineering, survival analysis, and environmental studies.