Abstract
We introduce a new model called the length-biased exponential distribution which become a fascinating new model in a number of research domains in recent years. By adding an extra shape parameter, a new generalised form that is coupled to the length-biased exponential distribution addressed in this work may be constructed, enhancing its utility. The new distribution is known as the new extension length-biased exponential distribution (NELBE). Its density function, as well as its survival and hazard rate curves, are all shown graphically. The study presented the quantile function, linear representations, and some other properties. We displayed and graphed the shapes of the distribution functions. When it came time to calculate the distribution parameters, we employed a total of six distinct estimating strategies. In order to compare and draw conclusions about the performance of the different estimators, a thorough numerical analysis was done. Here, two real data set on COVID-19 mortality rate was examined to show how adaptable and practical the suggested distribution is.