Optimization of Gamma–Power–Log–logistic distribution and its applications in modelling volume of oil spillage

Abstract

Oil spillage is one of the major problems in the Niger Delta region of Nigeria, which have affected human health and aquaculture. There is a need to estimate the volume of spill per incidence. Estimating the volume of crude oil after spill is a problem in environmental sciences. In this research, a newly-convoluted gamma–power generalized linear model (GLM), which was derived from Gamma–Power–Log–logistic distribution was developed. The proposed model was used to fit a regression model to estimate the spill volume of crude oil in the South–south geopolitical zone of Nigeria. Some statistical properties of the distribution such as, the transformation to a gamma distribution and the likelihood ratio test were derived. The Maximum Likelihood Estimation (MLE) technique, using generalized Newton Approximation with Expectation Maximization (EM) algorithm was used to obtain the model parameters and the consistency of the parameters estimated was justified by a simulation study. The simulation study result showed that the parameters estimated are consistent. The result of the likelihood ratio test (LRT) and other selection criteria adopted showed that the novel GPGLM outperformed other models. The LRT showed how much better the proposed model could be when compared to gamma and normal models as a good fit to bimodal skewed leptokurtic dependent response variable in a regression settings. The new model is an extension of the gamma model and would be very useful for modelling bimodal, skewed and leptokurtic dependent variable in a regression model. The study recommended that clean-up should be done promptly in order to achieve the Sustainable Development Goal of access to clean water and improved quality of life.