Square Transformed Half Normal Distribution with Its Properties and Applications

This paper introduces the Square Transformed Half-Normal Distribution (STHND), a new continuous distribution from the half-normal distribution through a square-root transformation.Key statistical properties-such as the PDF, CDF, quantile function, moments, and hazard rate are calculated in closed form.Compared to earlier half-normal extensions, the STHND has a poorer compromise of flexibility and simplicity.Monte Carlo simulations and applications to real and simulated datasets demonstrate its superior fit over five alternative distributions, based on AIC, BIC, CAIC, and HQIC.