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The occurrence of earthquakes is increasing almost every year in Indonesia. From January 2014 to December 2017, there was around 16,645 earthquakes with magnitude ≥4 Richter Scale occurred. This study is the first part of earthquake risk modeling that we conducted. This study aims to analyze the relationship of frequency and magnitude of the earthquakes by using Poisson Regression and Generalized Poisson Regression. The data used in this study is frequency and magnitude data of earthquakes occurred in Indonesia. The data were selected by selecting earthquakes with magnitude ≥4 Richter Scale in the period January 2014 to December 2017 (4 years). The dependent variable is frequency, meanwhile the magnitude is independent. The frequency of earthquakes is the rounded value of natural log (Ln) transformation of cumulative frequency of earthquakes occurred in time period, and tested that it follows poisson distribution. The Poisson Regression analysis was done for the first, then the analysis continued by using Generalized Poisson Regression to observe whether there is equidispersion effect. The result of two models was compared then continued by selecting the best model based on the smallest of Akaike Information Criterion (AIC). According to the result of Poisson Regression as well as Generalized Poisson Regression, the magnitude is significantly affect the frequency. Based on AIC, the best model of frequency-magnitude relationship is presented by Poisson Regression model, μ = exp (4.048 – 0.3935x). [ABSTRACT FROM AUTHOR]

This research focused on parameter estimation and hypothesis testing of Bivariate Zero-Inflated Poisson Inverse Gaussian Regression (BZIPIGR) type II. BZIPIGR model is a mixed Poisson distribution used to model data with excess-zero and overdispersion. The parameter estimation in this study used the Maximum Likelihood Estimation (MLE) method. The first derivative of the log-likelihood function from the BZIPIGR model had obtained not closed-form. Therefore, to maximize the likelihood function, it had used numerical iteration, namely the Berndt-Hall-Hall-Hausman (BHHH). The determination of the critical area and the significance of the model parameters had used the Maximum Likelihood Ratio Test (MLRT). [ABSTRACT FROM AUTHOR]

Generalized Poisson regression is a common model used for over/underdispersion count data. However, excess zeros in the observed data can create difficulties for this model. The zero-inflation regression model is a model that can be used to handle excess zeros on data. If the observational data is over/underdispersion and excess zero, then the Zero-Inflated Generalized Poisson regression (ZIGPR) is the proper model to use. This study aims to obtain the estimator of the BZIGP regression through the EM algorithm and to model data on stillbirths and maternal deaths in 91 sub-districts in Pekalongan Residency, Central Java. Because there are two response variables, the regression analysis used is Bivariate ZIGPR (BZIGPR). The BZIGPR discussed in this study is BZIGPR type II, where the two BZIGP type II marginal distributions have their parameter of zero inflation to be applied in a broader range. BZIGPR parameter estimation is done using the EM algorithm, while the hypothesis testing of the BZIGPR model is derived using the Maximum Likelihood Ratio Test (MLRT). The model generated in the BZIGPR consists of two parts, the log model and the logit model. The results showed an overdispersion and an underdispersion in maternal deaths and stillbirths data, respectively. Based on empirical studies, all predictor variables affect the two response variables significantly. [ABSTRACT FROM AUTHOR]