The Exponentiated Gumbel–Weibull {Logistic} Distribution with Application to Nigeria’s COVID-19 Infections Data

Abstract

A new flexible univariate probability distribution was defined in this paper. The new distribution is so called the ‘exponentiated Gumbel–Weibull {logistic} distribution’ and it arose by using the exponentiated Gumbel distribution to generate a generalized Weibull distribution using the logit function or the quantile function of the logistic distribution as a link. The new distribution was observed to be both unimodal and bimodal as well as exhibits various shape and tail properties consistent with data arising from several real life phenomena. A detail study of its statistical properties was carried out and the maximum likelihood method was used in the estimation of its parameters. The new distribution was applied in fitting the reported daily number of infections due to the COVID-19 pandemic in Nigeria. Five other datasets were further used to ascertain the flexibility of the new distribution in fitting data sets with different statistical properties.