Cauchy modified generalized exponential distribution: Estimation and Applications

Abstract

We present a unique probability model in this study called the Cauchy Modified Generalized Exponential Distribution. This model is formulated by combining the Cauchy family of distributions with the Modified Generalized Exponential Distribution as the baseline distribution. Our objective is to employ this model in the analysis of lifetime data. We've crafted formulas for various statistical functions, like skewness, kurtosis, survival function, quantile function, hazard rate function, distribution function, and probability density function. Additionally, we've integrated visual depictions of the probability density and hazard rate curves. We gathered a dataset that included notable earthquakes (magnitude 7.0 and higher) that the USGS had documented between 1990 and 2018. Our proposed model's effectiveness was evaluated by applying it to a global dataset covering significant earthquakes of the same magnitude range. The model parameters were estimated using maximum likelihood estimation. Several statistical measures were applied in order to confirm the validity of the model, including the Bayesian Information Criterion, Corrected Akaike's Information Criterion, the Hannan-Quinn Information Criterion, and Akaike's Information Criterion. Additionally, Q-Q and P-P plots were employed for validation. We used the Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises tests to evaluate how well our model fit the data. These tests were conducted to determine the suitability of our model for analyzing the provided earthquake data. Our empirical results indicate that, compared to alternative lifetime distributions, our suggested distribution not only exhibits a better fit but also provides increased flexibility for analyzing lifetime data. This study advances our understanding of earthquake patterns and contributes to the ongoing efforts in seismic risk assessment and mitigation strategies. All numerical calculations were performed using the R programming language.