Statistical Analysis and Several Estimation Methods of New Alpha Power-Transformed Pareto Model with Applications in Insurance

This article defines a new distribution using a novel alpha power-transformed method extension. The model obtained has three parameters and is quite effective in modeling skewed, complex, symmetric, and asymmetric datasets. The new approach has one additional parameter for the model. Certain distributional and mathematical properties are investigated, notably reliability, quartile, moments, skewness, kurtosis, and order statistics, and several approaches of estimation, notably the maximum likelihood, least square, weighted least square, maximum product spacing, Cramer-Von Mises, and Anderson Darling estimators of the model parameters were obtained. A Monte Carlo simulation study was conducted to evaluate the performance of the proposed techniques of estimation of the model parameters. The actuarial measures are computed for our recommended model. At the end of the paper, two insurance applications are illustrated to check the potential and utility of the suggested distribution. Evaluation using four selection criteria indicates that our recommended model is the most appropriate probability model for modeling insurance datasets.