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 hazard rate is proposed and called Arz distribution. This distribution is suggested based on the idea of mixture distributions. We investigate several properties of this distribution such as rth moment, moment generating function, skewness, coefficient of variation, kurtosis, index of dispersion, order statistics, Lorenz and Bonferroni curves, Gini index, stochastic ordering, Rényi entropy, mean deviations about mean and median. Also, the survival function, hazard function, mean residual life function, reversed hazard function, and odds function are provided with graphical representation. It is found that the hazard function has a bathtub shape even though the distribution has one parameter. The parameter of the distribution is estimated using maximum likelihood method. Application to COVID-19 data set is presented to show the flexibility of the suggested distribution. The application indicates that the proposed distribution is more flexible than some other competitive distributions in fitting such data.