Table 2 Some sub-families of the T–R{Y}–PS family of distributions
From: The T–R {Y} power series family of probability distributions
Distributions | cdf |
|---|---|
T–R{Y}–B | \( 1-\frac{{\left(1+\theta \left(1-{F}_T\left({Q}_Y\left({F}_R(x)\right)\right)\right)\right)}^m-1}{{\left(1+\theta \right)}^m-1},x\in \mathbb{R}. \) |
T–R{Y}–G | \( \frac{F_T\left({Q}_Y\left({F}_R(x)\right)\right)}{1-\theta \left(1-{F}_T\left({Q}_Y\left({F}_R(x)\right)\right)\right)},x\in \mathbb{R}. \) |
T–R{Y}–L | \( 1-\frac{\log \left(1-\theta \left(1-{F}_T\left({Q}_Y\left({F}_R(x)\right)\right)\right)\right)}{\log \left(1-\theta \right)},x\in \mathbb{R}. \) |
T–R{Y}–P | \( 1-\frac{{\mathrm{e}}^{\theta \left(1-{F}_T\left({Q}_Y\left({F}_R(x)\right)\right)\right)}-1}{{\mathrm{e}}^{\theta }-1},x\in \mathbb{R}. \) |