Table 1 Some models used to characterize the distribution of wind speeds

Rayleigh (Jung & Schindler, 2017; Katinas et al., 2018; Masseran, 2018; Mohammadi et al., 2017; Wang et al., 2016)

\(f(x,\alpha ) = \frac{x}{{\alpha^{2} }}exp\left[ { - \frac{1}{2}\left( {\frac{x}{\alpha }} \right)^{2} } \right]\)

Normal (Jung & Schindler, 2017; Mohammadi et al., 2017; Wang et al., 2016)

\(f\left( {x,\alpha ,\mu } \right) = \frac{1}{{\alpha \sqrt {2\pi } }}\exp \left[ { - \frac{1}{2}\left( {\frac{x - \mu }{\alpha }} \right)^{2} } \right]\)

Log normal (Alavi et al., 2016; Jung & Schindler, 2017; Masseran, 2018; Mohammadi et al., 2017; Wang et al., 2016)

\(f\left( {x,\alpha ,\mu } \right) = \frac{1}{{x\alpha \sqrt {2\pi } }}\exp \left[ { - \frac{1}{2}\left( {\frac{\ln \left( x \right) - \mu }{\alpha }} \right)^{2} } \right]\)

Truncated normal (Jung & Schindler, 2017; Wang et al., 2016)

\(\begin{gathered} f\left( {x,\alpha ,\mu } \right) = \frac{1}{{I\left( {\alpha ,\mu } \right)\alpha \sqrt {2\pi } }}\exp \left[ { - \frac{1}{2}\left( {\frac{x - \mu }{\alpha }} \right)^{2} } \right]\; \hfill \\ where \hfill \\ I\left( {\alpha ,\mu } \right) = \frac{1}{{\alpha \sqrt {2\pi } }}\int\limits_{0}^{\infty } {\exp \left[ { - \frac{1}{2}\left( {\frac{x - \mu }{\alpha }} \right)^{2} } \right]dx} \hfill \\ \end{gathered}\)

Logistic (Jung & Schindler, 2017; Mohammadi et al., 2017)

\(f\left( {x,\alpha ,\mu } \right) = \frac{1}{{\alpha \left[ {1 + \exp \left( {\frac{x - \mu }{\alpha }} \right)} \right]^{2} }}\exp \left( {\frac{x - \mu }{\alpha }} \right)\)

Log logistic (Alavi et al., 2016; Jung & Schindler, 2017; Mohammadi et al., 2017; Wang et al., 2016)

\(f\left( {x,\alpha ,\mu } \right) = \frac{1}{{x\alpha \left[ {1 + \exp \left( {\frac{\ln \left( x \right) - \mu }{\alpha }} \right)} \right]^{2} }}\exp \left( {\frac{\ln \left( x \right) - \mu }{\alpha }} \right)\)

Generalised extreme value (Alavi et al., 2016; Jung & Schindler, 2017; Mohammadi et al., 2017)

\(f\left( {x,\alpha ,k,\mu } \right) = \frac{1}{\alpha }\left[ {1 - \frac{k}{\alpha }\left( {x - \mu } \right)} \right]^{{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-0pt} k} - 1}} \exp \left\{ { - \left[ {1 - \frac{k}{\alpha }\left( {x - \mu } \right)} \right]^{{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-0pt} k}}} } \right\}\)

Nakagami (Alavi et al., 2016; Jung & Schindler, 2017; Mohammadi et al., 2017)

\(f\left( {x,\alpha ,k} \right) = \frac{{2k^{k} }}{{\Gamma \left( k \right)\alpha^{k} }}x^{2k - 1} \exp \left( { - \frac{k}{\alpha }x^{2} } \right)\)

Inverse Gaussian (Jung & Schindler, 2017; Masseran, 2018; Mohammadi et al., 2017)

\(f\left( {x,\alpha ,\mu } \right) = \sqrt {\frac{\alpha }{{2\pi x^{3} }}} \exp \left[ { - \frac{1}{2}\frac{\alpha }{x}\left( {\frac{x - \mu }{\mu }} \right)^{2} } \right]\)

Inverse Weibull (Akgül et al., 2016; Jung & Schindler, 2017)

\(f\left( {x,\alpha ,k} \right) = \frac{k}{\alpha }\left( {\frac{\alpha }{x}} \right)^{k + 1} \exp \left[ { - \left( {\frac{\alpha }{x}} \right)^{k} } \right]\)

Weibull (Alavi et al., 2016; Jung & Schindler, 2017; Katinas et al., 2018; Masseran, 2018; Mohammadi et al., 2017; Wang et al., 2016)

\(f\left( {x,\alpha ,k} \right) = \frac{k}{\alpha }\left( {\frac{x}{\alpha }} \right)^{k - 1} \exp \left[ { - \left( {\frac{x}{\alpha }} \right)^{k} } \right]\)