Examining the generalized odd log-Logistic Family : a regression compilation

Abstract

In this work, considering the family of distributions, generalized odd log-logistic-G, several applications have been proposed with different real data using regression models. The distri- butions of this family accommodate asymmetric, bimodal and heavy-tailed forms, showing flexibility when compared to other well-known generator distributions. Based on the generator family of distributions presented, regression models have been introduced with distinct sys- tematic structures, linking the explanatory variables through the parameters of the baseline distribution and all computational modeling is implemented using the R software. The first two applications involve two univariate distributions: Lindley and exponential. The first uses the novel generalized odd log-logistic Lindley distribution to evaluate data on the completed primary vaccination rate of COVID-19 in counties in the American state of Texas. The sec- ond uses the generalized odd log-logistic exponential distribution to investigate dengue fever weekly cases in the Federal District of Brazil. The other applications relied on the well-known continuous distributions, gamma, and Weibull distributions. The first applies the generalized odd log-logistic gamma distribution to agricultural data on yacon potatoes from a study in Peru. The following analysis employs the generalized odd log-logistic Weibull distribution to examine daily wind power generation data in Brazil. Monte Carlo simulations are used to eva- luate the accuracy of maximum likelihood estimates using a variety of measures. In order to determine the most suitable model, the research includes goodness-of-fit measures, diagnostics and residual analysis. Finally, the findings obtained utilizing various data sets demonstrated that the proposed models are a viable alternative to competing distributions.