Using The Maximum Likelihood And Bayesian Methods To Estimate The Time-Rate Function Of Earthquake Phenomenon

Abstract

In this research, we dealt with the study of the Non-Homogeneous Poisson process, which is one of the most important statistical issues that have a role in scientific development as it is related to accidents that occur in reality, which are modeled according to Poisson’s operations, because the occurrence of this accident is related to time, whether with the change of time or its stability. In our research, this clarifies the Non-Homogeneous hemispheric process and the use of one of these models of processes, which is an exponentiated - Weibull model that contains three parameters (α, β, σ) as a function to estimate the time rate of occurrence of earthquakes in Erbil Governorate, as the governorate is adjacent to two countries that fall within the seismic belt which are Turkey and Iran, which makes it not excluded from the arrival of seismic frequencies to it, where the three parameters of the above model were estimated in two ways which are the maximum likelihood method and the Bayesian method to find the time average of the occurrence of this phenomenon and a mean square error (MSE) was used to find out which methods are best in estimating the model parameters show that the Bayesian method is the best estimation method.