Extending Normality: A Case of Unit Distribution Generated from the Moments of the Standard Normal Distribution

This paper presents an important theorem, which shows that, heading from the moments of standard normal distribution, one can generate density functions originating a family models. Additionally, we discussed that different random variable domains are achieved with transformations. For instance, adopted moment order two, proposed and transformed it, enabled us to exemplify this class as unit distribution. We named it Alpha-Unit (AU) contains single positive parameter α (AU(α)∈[0,1]). presented its properties demonstrated two estimation methods for parameter, maximum likelihood estimator (MLE) uniformly minimum-variance unbiased (UMVUE) methods. In analyze statistical consistency estimators, Monte Carlo simulation study was carried out, in robustness demonstrated. As real-world application, sets data, first regarding dynamics Chilean inflation post-military period, other daily relative humidity air Atacama Desert. both cases presented, AU model is competitive, whenever data present range greater than 0.4 extremely heavy asymmetric tail. compared our commonly used models, such beta, Kumaraswamy, logit-normal, simplex, unit-half-normal, unit-Lindley distributions.