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Table 4 Different TR{Y}–B distributions

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

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