In this paper, the class of T-R {generalized lambda} families of distributions based on the quantile of generalized lambda distribution has been proposed using the T-R{Y} framework. In the development of the T-R{Y} framework, the support of Y and T must be the same. It is typical that the random variable Y has one type of support and T is restricted to the same support. Taking Y to be a generalized lambda random variable leads to three different types of supports, thus, making the choice of the generator T to be much more broad and flexible. This is interesting and unique. By allowing T with different supports makes the T-R{generalized lambda} a desirable method for generating new versatile and broad families of generalized distributions for any given random variable R. Some general properties of these families of distributions are studied. Four members of the T-R{generalized lambda} families of distributions are derived. The shapes of these distributions can be symmetric, skewed to the left, skewed to the right, or bimodal. Two real life data sets are applied to illustrate the flexibility of the distributions.

中文翻译：

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广义λ分布的分位数引起的分布族

在本文中，使用TR {Y}框架提出了基于广义Lambda分布的分位数的TR {generalized lambda}族族的类别。在TR {Y}框架的开发中，Y和T的支持必须相同。通常，随机变量Y具有一种支持类型，并且T限于相同的支持类型。将Y用作广义的Lambda随机变量会导致三种不同类型的支持，从而使生成器T的选择更加广泛和灵活。这是有趣而独特的。通过允许T具有不同的支持，TR {generalized lambda}成为一种理想的方法，可以为任何给定的随机变量R生成新的通用分布族群，并且具有广泛的用途。研究了这些分布族的一些一般性质。派生了TR {generalized lambda}族的四个成员。这些分布的形状可以是对称的，向左偏斜，向右偏斜或双峰。应用两个实际数据集来说明分布的灵活性。