Family of generalized gamma distributions: Properties and applications

Abstract

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

Keywords

• T-R{Y} framework,quantile function,Shannon’s entropy,bimodality

References

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