Derivation of a New Odd Exponential-Weibull Distribution

Abstract

The study of statistical distributions has led to the development of numerous extensions of well-known continuous distributions to enhance their flexibility and applicability across various fields. In this paper, we introduce a new three-parameter distribution known as the Odd Exponential-Weibull (OE-W) distribution, which extends the traditional Weibull distribution by incorporating  additional parameter. We thoroughly investigate the mathematical properties of the OE-W distribution, deriving explicit formulas for the quantile function, moments, moment-generating function, survival function, hazard function, entropy, and order statistics. Parameter estimation is conducted using the maximum likelihood estimation (MLE) method, which is known for its robustness. To assess the reliability and accuracy of these parameter estimates, a Monte Carlo simulation study is performed. The simulation results indicate that the MLE method consistently yields reliable and accurate estimates for the parameters of the OE-W distribution. The introduction of this new distribution provides a valuable tool for modeling and analyzing data in fields such as reliability engineering and survival analysis, where flexible and accurate probability distributions are crucial.