Different Methods for Estimating Default Parameters of Alpha Power-Transformed Power Distributions Using Record-Breaking Data

The current study addresses the estimation of the default parameters of alpha power-transformed power (APTPO) distributions. For the location and scale parameters of the APTPO distributions, we provide coefficients for both the best linear unbiased estimators (BLUE) and the best linear invariant estimators (BLIE) methods. Furthermore, we establish a forecast for future records. The parameters of the APTPO distribution are estimated using the maximum likelihood estimation method (MLE). The goodness-of-fit test (using Akaike information criterion (AIC)) is computed using both the inter-record time sequence and the entire sample. Also, we utilize a simulation approach to demonstrate the practicality and benefits of our perspective. Finally, we demonstrate the accuracy of these parameters and the performance of estimators through a real-life example.