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Table 7 Different TR{Y}–P distributions

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

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