A New Four Parameter Extended Exponential Distribution with Statistical Properties and Applications

In this work, we introduce a novel generalization of the extended exponential distribution with four parameters through the Kumaraswamy family. The proposed model is referred to as the Kumaraswamy extended exponential (KwEE). The significance of the suggested distribution from its flexibility in applications and data modeling. As specific sub-models, it includes the exponential, Kumaraswamy exponential, Kumaraswamy Lindley, Lindley, extended exponential, exponentiated Lindley, gamma and generalized exponential distributions. The representation of the density function, quantile function, ordinary and incomplete moments, generating function, and reliability of the KwEE distribution are all derived. The maximum likelihood approach is used to estimate model parameters. A simulation study for maximum likelihood estimates was used to investigate the behaviour of the model parameters. A numerical analysis is performed for various sample sizes and parameter values to analyze the behaviour of estimates using accuracy measures. According to a simulated investigation, the KwEE's maximum likelihood estimates perform well with increased sample size. We provide two real-world examples utilizing applied research to demonstrate that the new model is more effective.