Table 9 Competitive distributions.

Lomax–Gumbel{Fréchet}

L-G{F}

\(1-{\left( 1+\gamma e^x\right) ^{-\alpha }}\)

¹²

Compound inverse Rayleigh

CIR

\(\left( 1+\frac{ x^{-2}}{\alpha }\right) ^{-\beta }\)

¹³

Power inverse Lomax

PIL

\(\left( 1+\frac{\beta }{x^{\theta }}\right) ^{-\alpha }\)

¹⁴

New weighted Lomax

NWL

\(1-\left( \frac{\beta \left( \frac{e^x}{\beta }+1\right) }{\beta +1}\right) ^{-\alpha }\)

¹⁵