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Table 2 Some sub-families of the TR{Y}–PS family of distributions

From: The TR {Y} power series family of probability distributions

Distributionscdf
TR{Y}–B\( 1-\frac{{\left(1+\theta \left(1-{F}_T\left({Q}_Y\left({F}_R(x)\right)\right)\right)\right)}^m-1}{{\left(1+\theta \right)}^m-1},x\in \mathbb{R}. \)
TR{Y}–G\( \frac{F_T\left({Q}_Y\left({F}_R(x)\right)\right)}{1-\theta \left(1-{F}_T\left({Q}_Y\left({F}_R(x)\right)\right)\right)},x\in \mathbb{R}. \)
TR{Y}–L\( 1-\frac{\log \left(1-\theta \left(1-{F}_T\left({Q}_Y\left({F}_R(x)\right)\right)\right)\right)}{\log \left(1-\theta \right)},x\in \mathbb{R}. \)
TR{Y}–P\( 1-\frac{{\mathrm{e}}^{\theta \left(1-{F}_T\left({Q}_Y\left({F}_R(x)\right)\right)\right)}-1}{{\mathrm{e}}^{\theta }-1},x\in \mathbb{R}. \)