In fitting a continuous bounded data, the generalized beta (and several variants of this distribution) and the two-parameter Kumaraswamy (KW) distributions are the two most prominent univariate continuous distributions that come to our mind. There are some common features between these two rival probability models and to select one of them in a practical situation can be of great interest. Consequently, in this paper, we discuss various methods of selection between the generalized beta proposed by Libby and Novick (1982) (LNGB) and the KW distributions, such as the criteria based on probability of correct selection which is an improvement over the likelihood ratio statistic approach, and also based on pseudo-distance measures. We obtain an approximation for the probability of correct selection under the hypotheses HLNGB and HKW , and select the model that maximizes it. However, our proposal is more appealing in the sense that we provide the comparison study for the LNGB distribution that subsumes both types of classical beta and exponentiated generators (see, for details, Cordeiro et al. 2014; Libby and Novick 1982) which can be a natural competitor of a two-parameter KW distribution in an appropriate scenario.

翻译：在拟合连续有界数据时，广义贝塔分布（及其多种变体）与双参数Kumaraswamy（KW）分布是我们首要考虑的两类最具代表性的单变量连续分布。这两种竞争性概率模型存在共同特征，在实际应用中选择其中之一具有重要研究价值。为此，本文探讨了Libby与Novick（1982）提出的广义贝塔分布（LNGB）与KW分布之间的多种选择方法，包括基于正确选择概率的准则（该准则优于似然比统计量方法），以及基于伪距离度量的方法。我们在假设HLNGB与HKW下推导了正确选择概率的近似表达式，并选择最大化该概率的模型。然而，本研究的独到之处在于：针对LNGB分布（该分布涵盖了经典贝塔分布与指数生成模型两类形式，详见Cordeiro等2014年文献及Libby与Novick 1982年文献），我们提供了系统的比较研究，该分布可在适当场景下成为双参数KW分布的天然竞争者。