(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, a new modifying method has been introduced by adding an extra parameter to generate a new family of distributions that has more flexibility and better model fitting. A special case has been considered; the exponential distribution. All the main properties of the new modified exponential distribution are derived, including the CDF, PDF, and quantile function. The maximum likelihood estimation method is used to estimate unknown parameters. The modified exponential distribution has been applied to two-lifetime data sets to illustrate its efficiency.