An Alternative One-Parameter Distribution for Bounded Data Modeling Generated from the Lambert Transformation

The beta and Kumaraswamy distributions are two of the most widely used for modeling bounded data. When histogram a certain dataset exhibits increasing or decreasing behavior, one-parameter such as power, Marshall–Olkin extended uniform skew-uniform become viable alternatives. In this article, we propose new distribution data, Lambert-uniform distribution. proposal can be considered natural alternative to well known in statistical literature and, scenarios, even two-parameter distributions. We show that density function tends positive finite values at ends support, behavior favors good performance scenarios. raw moments derived from moment-generating describe skewness kurtosis behavior. quantile is expressed closed form terms Lambert W function, which allows reparameterizing involved parameter represents qth quantile. Thus, analysis range variable, set covariates available, regression model relates response linear predictor through link function. estimation carried out using maximum likelihood method estimators evaluated simulation experiments. Finally, three application examples order illustrate usefulness proposal.