Table 7 Different T–R{Y}–P distributions
From: The T–R {Y} power series family of probability distributions
Distributions | cdf |
|---|---|
T–R{exponential}–P | \( 1-\frac{{\mathrm{e}}^{\theta \left(1-{F}_T\left(-\log \left(1-{F}_R(x)\right)\right)\right)}-1}{{\mathrm{e}}^{\theta }-1},x\in \mathbb{R}. \) |
T–R{logistic}–P | \( 1-\frac{{\mathrm{e}}^{\theta \left(1-{F}_T\left(\log \left({F}_R(x)/\left(1-{F}_R(x)\right)\right)\right)\right)}-1}{{\mathrm{e}}^{\theta }-1},x\in \mathbb{R}. \) |
T–R{extreme value}–P | \( 1-\frac{{\mathrm{e}}^{\theta \left(1-{F}_T\left(\log \left(-\log \left(1-{F}_R(x)\right)\right)\right)\right)}-1}{{\mathrm{e}}^{\theta }-1},x\in \mathbb{R}. \) |
T–R{log logistic}–P | \( 1-\frac{{\mathrm{e}}^{\theta \left(1-{F}_T\left({F}_R(x)/\left(1-{F}_R(x)\right)\right)\right)}-1}{{\mathrm{e}}^{\theta }-1},x\in \mathbb{R}. \) |
T–R{uniform}–P | \( 1-\frac{{\mathrm{e}}^{\theta \left(1-{F}_T\left({F}_R(x)\right)\right)}-1}{{\mathrm{e}}^{\theta }-1},x\in \mathbb{R}. \) |