A new generalized Logistic class of distributions: Properties and applications on flood and earthquake data sets with bivariate extension

For univariate and bi-variate data, we propose a new generalized logistic class of distributions exible enough to exhibit monotone and non-monotone hazard rates shapes. The physical interpretation of the new family preludes in the context of series-parallel structures. Its mathematical features, including a valuable expansion for the density, explicit formulations for the quantile function, ordinary and incomplete moments, and generating function, are all derived. The parameter estimation of the new family is done using the maximum likelihood method. One of the unique model, called the generalized logistic Burr-III, is thoroughly investigated in applied sense. The exible density and hazard rate shapes capacitates the model to be applicable in extreme value theory. For univariate case, two real-life data sets related to hydrology and seismic activity have been employed to solidify the superiority of the proposed distribution to ve well established families. For bivariate data, initially a bivariate extension of the proposed family is established analytically with the help of empirical ndings. Then, a real bi-variate data related to operational lifespan of two components of a computer, has been studied using bivariate generalized logistic Burr-III model and the results are reported.