Efficient Modeling of Nonmonotonic Hazard Rates: Exponential-Type Weibull Distribution With COVID-19 Mortality Case Study

Accurate modeling of survival data with nonmonotonic hazards is crucial for epidemiology and reliability studies. We introduce the flexible exponential-type family (FETF) and its parsimonious two-parameter submodel (the exponential-type Weibull, ETW) that can capture both bathtub-shaped and unimodal hazard rates. We derive closed-form and convergent series representations for key properties, including moments, quantiles, survival and hazard functions, mean residual life, and Shannon entropy, with the mode obtained numerically. Parameters are estimated by maximum likelihood; inference uses the observed Fisher information together with practical guidance on starting values and convergence diagnostics. Application to anonymized COVID-19 mortality data shows ETW provides a competitive or improved fit relative to several competitors (Weibull, inverse Weibull, transmuted inverse Weibull, and alpha power Weibull), supported by likelihood-ratio comparisons, relative improvements in information criteria (ΔAIC = −2.59; ΔBIC = −7.51), and favorable goodness-of-fit results (KSD = 0.049; parametric bootstrap p>0.5 reported). Monte Carlo simulations (B = 1000) quantify estimator bias and MSE across representative parameter settings and demonstrate consistent model-selection performance. The ETW thus provides a parsimonious, reproducible, and tractable framework for modeling complex survival data.