On a New Two-parameter Weighted Exponential Distribution and Its Application to the COVID-19 and Censored Data

Abstract

Simple and flexible lifetime distributions are appreciated by practitioners in all applied fields. They allow the construction of fairly manageable statistical models. In this article, a new simple lifetime distribution involving two parameters is proposed. It is based on a simple modification of the construction of the so-called weighted exponential distribution, by replacing the exponential distribution with the Erlang distribution. This choice is motivated by solid mathematical and physical interpretations. The new distribution is naturally named the new two-parameter weighted distribution. In the first part, we present the main mathematical properties of this distribution, with an emphasis on the flexibility of the probabilistic functions, the closed forms of various moments, and the analysis
of the skewness and kurtosis coefficients. The remaining part is devoted to the associated model, showing how it can be applied in a real statistical scenario dealing with data. In this regard, four data sets are considered, two complete and two censored data sets; one on the survival times of guinea pigs injected with a certain bacteria, one on the COVID-19 daily death rate in Israel, one on
censored data about survival times of patients infected with HIV, and one on censored data about remission times for leukemia patients treated with a special drug. The performance of the new model is compared with that of the weighted exponential, two-parameter weighted exponential and extended weighted exponential models. The obtained comparison results are quite favorable to the proposed methodology.