Table I.

Expression of the nine investigated PDFs. Here $\varphi \left(z\right)=\exp (-z^2∕2)∕\sqrt{2\pi }$ is the PDF of a standardized normal distribution, $\Gamma \left(m\right)={\int }_0^{\infty }{x}^{m-1}{e}^{-x}dx$ is the gamma function, ϕ_logis(z) = e^z(1 + e^z)^–2 is the PDF of a standardized logistic distribution.

Family	Probability Density Function (r ≥ 0 unless specified)	Parameter interpretation
Rayleigh (RA)	$f(r;\sigma )=\frac{r}{{\sigma }^2}\exp (-\frac{r^2}{2{\sigma }^2})$	σ > 0: scale
Normal (NM)	$f(r;\mu ,\sigma )=\frac{1}{\sigma }\varphi \left(\frac{r-\mu }{\sigma }\right),r\in \mathbb{R}$	μ: mean; σ > 0: standard deviation
Lognormal (LM)	$f(r;\mu ,\sigma )=\frac{1}{\sigma r}\varphi \left(\frac{\ln r-\mu }{\sigma }\right),r>0$	μ: location σ > 0: scale
Nakagami (NA)	$f(r;m,\Omega )=\frac{2m^m{r}^{2m-1}}{\Gamma \left(m\right){\Omega }^m}\exp (-\frac{m}{\Omega }{r}^2)$	m ≥ 0.5: shape Ω > 0: scale
Weibull (WE)	$f(r;\alpha ,\beta )=\frac{\beta }{{\alpha }^{\beta }}{r}^{\beta -1}\exp [-{\left(\frac{r}{\alpha }\right)}^{\beta }]$	α > 0: scale β > 0: shape
Loglogistic (LL)	$f(r;\mu ,\sigma )=\frac{1}{\sigma r}{\varphi }_{logis}\left(\frac{\ln r-\mu }{\sigma }\right),r>0$	μ: location σ > 0: scale
Gamma (GA)	$f(r;a,b)=\frac{1}{b^a\Gamma \left(a\right)}{r}^{a-1}\exp (-\frac{r}{b})$	a > 0: shape b > 0: scale
Generalized extreme value (GE)	$f(r;k,\mu ,\sigma )=\frac{1}{\sigma }\exp [-{(1+k\frac{r-\mu }{\sigma })}^{-\frac{1}{k}}]{(1+k\frac{r-\mu }{\sigma })}^{-1-\frac{1}{k}}$ with $1+k\frac{r-\mu }{\sigma }>0$	k ≠ 0: shape μ: location σ > 0: scale
Generalized gamma (GG)	$f(r;a,b,c)=\frac{c{r}^{ac-1}}{b^{ac}\Gamma \left(a\right)}\exp [-{\left(\frac{r}{b}\right)}^c]$	a > 0, c > 0: shape b > 0: scale