Table 5 Different T–R{Y}–G distributions
From: The T–R {Y} power series family of probability distributions
Distributions | cdf |
|---|---|
T–R{exponential}–G | \( \frac{F_T\left(-\log \left(1-{F}_R(x)\right)\right)}{1-\theta \left(1-{F}_T\left(-\log \left(1-{F}_R(x)\right)\right)\right)},x\in \mathbb{R}. \) |
T–R{logistic}–G | \( \frac{F_T\left(\log \left({F}_R(x)/\left(1-{F}_R(x)\right)\right)\right)}{1-\theta \left(1-{F}_T\left(\log \left({F}_R(x)/\left(1-{F}_R(x)\right)\right)\right)\right)},x\in \mathbb{R}. \) |
T–R{extreme value}–G | \( \frac{F_T\left(\log \left(-\log \left(1-{F}_R(x)\right)\right)\right)}{1-\theta \left(1-{F}_T\left(\log \left(-\log \left(1-{F}_R(x)\right)\right)\right)\right)},x\in \mathbb{R}. \) |
T–R{log logistic}–G | \( \frac{F_T\left({F}_R(x)/\left(1-{F}_R(x)\right)\right)}{1-\theta \left(1-{F}_T\left({F}_R(x)/\left(1-{F}_R(x)\right)\right)\right)},x\in \mathbb{R}. \) |
T–R{uniform}–G | \( \frac{F_T\left({F}_R(x)\right)}{1-\theta \left(1-{F}_T\left({F}_R(x)\right)\right)},x\in \mathbb{R}. \) |