Alpha Power Transformed Extended Exponential Distributione

Abstract

This study presents the Marshall-Olkin Alpha Power Transformed Extended Exponential Distribution, a new statistical model that improves the flexibility of the standard exponential distribution using the Marshall-Olkin Alpha Power Transformed Extended-X family of distributions. MOAPTEEx distribution depends on the parameters θ, λ, and α. The lack of closed-form solutions and the requirement for numerical methods are highlighted as we examine the Maximum Likelihood Estimation (MLE) method for parameter estimation. The performance of many estimating strategies, such as maximum product spacing (MPS), least squares (LS), and MLE, across a range of sample sizes is assessed; this is done using a Monte Carlo simulation exercise. The results show that MLE is the most reliable method, particularly for larger samples, while MPS performs worse for smaller samples. Applications to actual datasets provide additional validation of the MOAPTEEx distribution, showing its efficacy in simulating fiber strength datasets where outer-performed the other competing models.