A Flexible Truncated (u,v)-Half-Normal Distribution: Properties, Estimation and Applications

Abstract

This study introduces the truncated $(u,v)$-half-normal distribution, a novel probability model defined on the bounded interval $(u,v)$, with parameters $\sigma$ and b. This distribution is designed to model processes with restricted domains, ensuring realistic and analytically tractable outcomes. Some key properties of the proposed model, including its cumulative distribution function, probability density function, survival function, hazard rate, and moments, are derived and analyzed. Parameter estimation of $\sigma$ and b is achieved through a hybrid approach, combining maximum likelihood estimation (MLE) for $\sigma$ and a likelihood-free-inspired technique for b. A sensitivity analysis highlighting the dependence of $\sigma$ on b, and an optimal estimation algorithm is proposed. The proposed model is applied to two real-world data sets, where it demonstrates superior performance over some existing models based on goodness-of-fit criteria, such as the known AIC, BIC, CAIC, KS, AD, and CvM statistics. The results emphasize the model’s flexibility and robustness for practical applications in modeling data with bounded support.