In this paper, a family of generalized gamma distributions, T-gamma family, has been proposed using the T-R { Y} framework. The family of distributions is generated using the quantile functions of uniform, exponential, log-logistic, logistic and extreme value distributions. Several general properties of the T-gamma family are studied in details including moments, mean deviations, mode and Shannon's entropy. Three new generalizations of the gamma distribution which are members of the T-gamma family are developed and studied. The distributions in the T-gamma family are very flexible due to their various shapes. The distributions can be symmetric, skewed to the right, skewed to the left, or bimodal. Four data sets with various shapes are fitted by using members of the T-gamma family of distributions.
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