From: The T–R {Y} power series family of probability distributions
Distributions | cdf |
---|---|
T–R{exponential}–B | \( 1-\frac{{\left(1+\theta \left(1-{F}_T\left(-\log \left(1-{F}_R(x)\right)\right)\right)\right)}^m-1}{{\left(1+\theta \right)}^m-1},x\in \mathbb{R}. \) |
T–R{logistic}–B | \( 1-\frac{{\left(1+\theta \left(1-{F}_T\left(\log \left({F}_R(x)/\left(1-{F}_R(x)\right)\right)\right)\right)\right)}^m-1}{{\left(1+\theta \right)}^m-1},x\in \mathbb{R}. \) |
T–R{extreme value}–B | \( 1-\frac{{\left(1+\theta \left(1-{F}_T\left(\log \left(-\log \left(1-{F}_R(x)\right)\right)\right)\right)\right)}^m-1}{{\left(1+\theta \right)}^m-1},x\in \mathbb{R}. \) |
T–R{log logistic}–B | \( 1-\frac{{\left(1+\theta \left(1-{F}_T\left({F}_R(x)/\left(1-{F}_R(x)\right)\right)\right)\right)}^m-1}{{\left(1+\theta \right)}^m-1},x\in \mathbb{R}. \) |
T–R{uniform}–B | \( 1-\frac{{\left(1+\theta \left(1-{F}_T\left({F}_R(x)\right)\right)\right)}^m-1}{{\left(1+\theta \right)}^m-1},x\in \mathbb{R}. \) |