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.
