Arz Distribution: A Novel One Parameter Model with Bathtub-Shaped Hazard Rate and Application on Covid-19

In this paper, a novel one parameter model with bathtub-shaped hazardrate is proposed and called Arz distribution. This distribution is suggestedbased on the idea of mixture distributions. We investigate several propertiesof this distribution such as rth moment, moment generating function, skew-ness, coe?cient of variation, kurtosis, index of dispersion, order statistics,Lorenz and Bonferroni curves, Gini index, stochastic ordering, R?enyi en-tropy, mean deviations about mean and median. Also, the survival function,hazard function, mean residual life function, reversed hazard function, andodds function are provided with graphical representation. It is found thatthe hazard function has a bathtub shape even though the distribution hasone parameter. The parameter of the distribution is estimated using maxi-mum likelihood method. Application to COVID-19 data set is presented toshow the ?exibility of the suggested distribution. The application indicatesthat the proposed distribution is more ?exible than some other competitivedistributions in ?tting such data.