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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.

Families of distributions arising from the quantile of generalized lambda distribution