In this paper, two new general families of distributions supported on the unit interval are introduced. The proposed families include several known models as special cases and define at least twenty (each one) new special models. Since the list of well-being indicators may include several double bounded random variables, the applicability for modeling those is the major practical motivation for introducing the distributions on those families. We propose a parametrization of the new families in terms of the median and develop a shiny application to provide interactive density shape illustrations for some special cases. Various properties of the introduced families are studied. Some special models in the new families are discussed. In particular, the complementary unit Weibull distribution is studied in some detail. The method of maximum likelihood for estimating the model parameters is discussed. An extensive Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. Applications to the literacy rate in Brazilian and Colombian municipalities illustrate the usefulness of the two new families for modeling well-being indicators.

在本文中，介绍了支持单位区间的两个新的一般分布族。提议的系列包括几个已知模型作为特例，并定义了至少二十个（每一个）新的特殊模型。由于福利指标列表可能包括几个双界随机变量，因此对这些变量进行建模的适用性是引入这些家庭分布的主要实际动机。我们建议根据中位数对新系列进行参数化，并开发一个闪亮的应用程序，为一些特殊情况提供交互式密度形状插图。研究了引入族的各种性质。讨论了新系列中的一些特殊型号。特别是，对互补单位 Weibull 分布进行了一些详细的研究。讨论了估计模型参数的最大似然法。进行了广泛的蒙特卡罗实验以评估这些估计器在有限样本中的性能。巴西和哥伦比亚城市的识字率应用说明了这两个新家庭对幸福指数建模的有用性。