Table 3 Some members of the T-X\(^{\theta }\) family.
Distribution of x | cdf | Range of x | Abbreviation |
|---|---|---|---|
Uniform-X \(^{\theta }\) beta \(^{1}\) | \(I_{x^{\theta +1} }(\alpha , \beta )\) | \(0<x<1\) | U-X\(^{\theta }\)B |
Beta-X\(^{\theta }\) uniform | \(x^{\theta }\left( I_{x }(\alpha , \beta ) \right)\) | \(0<x<1\) | B-X\(^{\theta }\)U |
Beta-X\(^{\theta }\) Kumaraswamy | \(I_{x^{\theta } \left( 1-\left( 1-x^{\lambda }\right) ^{\gamma }\right) }(\alpha ,\beta )\) | \(0<x<1\) | B-X\(^{\theta }\)Ku |
Exponential-X\(^{\theta }\) gamma | \(1-e^{-\frac{\lambda x^{\theta } \gamma (\alpha ,\frac{x}{\beta })}{\Gamma (\alpha )}}\) | \(x>0\) | E-X\(^{\theta }\)G |
Gamma-X\(^{\theta }\) Exponential | \(\dfrac{1}{\Gamma (\alpha )}{\gamma \left( \alpha ,\frac{x^{\theta }\left( 1-e^{- x}\right) }{\beta }\right) }\) | \(x>0\) | G-X\(^{\theta }\)E |
Gamma-X\(^{\theta }\) Lomax | \(\dfrac{1}{\Gamma (\alpha )}{\gamma \left( \alpha ,\frac{\left( 1-(x+1)^{-c}\right) x^{\theta }}{\beta }\right) }\) | \(x>0\) | G-\(X^{\theta }\)L |
Burr-X\(^{\theta }\) Exponential | \(1-\left( 1+x^{\theta }\left( 1-e^{-\alpha x}\right) \right) ^{-\beta }\) | \(x>0\) | Burr\(X^{\theta }\)E |
