Alpha Power Transformed Half Normal Distribution with Its Properties and Applications

The study aims to propose a new continuous probability distribution named Alpha Power Transformed Half-Normal Distribution by applying alpha power transformation method to Half normal distribution. Several vigorous statistical andmathematical properties of new distribution are derived. Simulation studies are conducted to evaluate their performance, and comparative model fitting is carried out using real and simulated datasets. The study employs the alpha power transformation technique, simulation experiments, and goodness-of-fit measures to compare the new distribution with five existing distributions. Results indicate that the proposed model provides a superior fit to two real-world datasets and one simulated dataset compared to five competing distributions. The hazard function of the new distribution exhibits highly flexible forms, enhancing its applicability to various lifetime and reliability data. The Alpha Power Transformed Half-Normal Distribution represents a significant contribution to probability and statistical theory. Its flexibility and strong empirical performance suggest its potential for broad application, and further testing on diverse life datasets is recommended.