Table 2 Probability distribution functions appeared in the literature for solvent extraction systems23,32.
Name | Formula |
|---|---|
Normal | \(\:{P}_{n}\left(d\right)=\frac{1}{\sqrt{2\pi\:}\alpha\:}\text{exp}\left[-{\left(\frac{d-\beta\:}{\sqrt{2}\alpha\:}\right)}^{2}\right]\) |
Log-normal | \(\:{P}_{n}\left(d\right)=\frac{1}{\sqrt{2\pi\:}d\alpha\:}\text{exp}\left[-{\left(\frac{\text{ln}d-\beta\:}{\sqrt{2}\alpha\:}\right)}^{2}\right]\) |
Weibull | \(\:{P}_{n}\left(d\right)=\alpha\:\beta\:{d}_{i}^{\alpha\:-1}\text{e}\text{x}\text{p}(-\beta\:{d}_{i}^{\alpha\:})\) |
Gamma | \(\:{P}_{n}\left(d\right)=\frac{\beta\:}{{\Gamma\:}\left(\alpha\:+1\right)}{d}^{\alpha\:}\text{exp}(-\beta\:d)\) |
