Estimating the Parameters of the Odd Lomax Exponential Distribution

Abstract

In this study, we introduce two methods for estimation of the unknown parameters of the Odd Lomax Exponential $(OLE)$ distribution are Least Squares Estimation $(LSE)$ and Maximum Likelihood Estimation $(MLE)$. Some statistical functions and mathematical properties were derived for which investigated from distribution’s flexibility . Through Monte Carlo simulations we investigated the performance of the estimate for these parameters, and us comparison these estimations in terms of bias and mean squared error $(MSE)$ for various sample sizes and four different scenarios of initial parameter values for two methods. Our analysis revealed that least square estimation consistently outperformed on $MLE$, yielding lower MSE values. Additionally, both two methods demonstrated decreasing in criteria values with increasing sample size, indicating improved accuracy for larger datasets. To evaluate the applicability of the $OLE$ distribution, we applied it to two types of dataset in the reliability engineering field. All computational and graphics in this work were performed in a Matlab, 23b code.