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Table 5 Different TR{Y}–G distributions

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

Distributionscdf
T–R{exponential}–G\( \frac{F_T\left(-\log \left(1-{F}_R(x)\right)\right)}{1-\theta \left(1-{F}_T\left(-\log \left(1-{F}_R(x)\right)\right)\right)},x\in \mathbb{R}. \)
TR{logistic}–G\( \frac{F_T\left(\log \left({F}_R(x)/\left(1-{F}_R(x)\right)\right)\right)}{1-\theta \left(1-{F}_T\left(\log \left({F}_R(x)/\left(1-{F}_R(x)\right)\right)\right)\right)},x\in \mathbb{R}. \)
TR{extreme value}–G\( \frac{F_T\left(\log \left(-\log \left(1-{F}_R(x)\right)\right)\right)}{1-\theta \left(1-{F}_T\left(\log \left(-\log \left(1-{F}_R(x)\right)\right)\right)\right)},x\in \mathbb{R}. \)
TR{log logistic}–G\( \frac{F_T\left({F}_R(x)/\left(1-{F}_R(x)\right)\right)}{1-\theta \left(1-{F}_T\left({F}_R(x)/\left(1-{F}_R(x)\right)\right)\right)},x\in \mathbb{R}. \)
TR{uniform}–G\( \frac{F_T\left({F}_R(x)\right)}{1-\theta \left(1-{F}_T\left({F}_R(x)\right)\right)},x\in \mathbb{R}. \)