Table 2.

Candidate model distributions and their functional forms

Name of PDF	Functional form	Parameters
Gaussian	$f(x/\mu ,\sigma )=\frac{1}{\sqrt{2\pi }\sigma }{e}^{-\frac{{(x-\mu )}^2}{2{\sigma }^2}}$	μ and σ are the mean and standard deviation respectively
Lognormal	$f(x/\mu ,\sigma )=\frac{1}{x\sqrt{2\pi }\sigma }{e}^{-\frac{{(\ln (x)-\mu )}^2}{2{\sigma }^2}}$	σ and eμ are shape and scale parameters. Defined for x > 0.
Log-logistic	$f\left(x/\alpha ,\beta \right)=\frac{\left(\alpha /\beta \right){\left(x/\beta \right)}^{\left(\alpha -1\right)}}{{\left(1+{\left(x/\beta \right)}^{\alpha }\right)}^2}$	α is the shape parameter and β is the scale parameters. x,α,β > 0.
Gamma	$f\left(x/\alpha ,\beta \right)=\frac{{\beta }^{\alpha }{x}^{\left(\alpha -1\right)}{e}^{-\mathit{x\beta }}}{\Gamma \left(\alpha \right)}$	α is the shape parameter and β is the inverse scale parameter. x,α,β > 0.
Weibull	$f\left(x/\alpha ,\beta \right)=\alpha {\mathit{\beta x}}^{\left(\alpha -1\right)}{e}^{-x^{\alpha }\beta }$	α is the shape parameter and β is the scale parameters. x,α,β > 0.