New Statistical Properties for Beta Inverted Exponential Distribution and Application on Covid-19 Cases in Saudi Arabia

Abstract

In this article new statistical properties of the beta inverted exponential distribution are investigated. The harmonic mean, mode, quantile function, median, skewness as well as kurtosis and interquartile range are studied. Important measures, which have a wide range of application in many fields, are considered. Among these measures stress\textendash strength reliability and R{\'{e}}nyi and Shannon entropies as well as order statistics. Also, the maximum likelihood estimation for the unknown parameters, survival and hazard functions are derived based on complete samples. The performance of the estimators is considered in terms of their biases and mean square error via Monte Carlo simulation. The potentiality of this distribution is illustrated through the daily COVID-19 cases observed in Jeddah, Saudi Arabia from $2^{nd}$ May to $6^{th}$ July 2020 as well as two other real data sets.