User:Dhatfield/Sandbox Rosin-Rammler distribution

Rosin-Rammler distribution

The Weibull distribution, now named for Waloddi Weibull was first identified by Fréchet (1927) and first applied by Rosin & Rammler (1933) to describe particle size distributions. It is still widely used in mineral processing to describe particle size distributions in comminution processes.

$f(x;P_{\rm {80}},m)={\begin{cases}1-e^{ln\left(0.2\right)\left({\frac {x}{P_{\rm {80}}}}\right)^{m}}&x\geq 0,\\0&x<0,\end{cases}}$

where

$x$: Particle size

$P_{\rm {80}}$: 80^th percentile of the particle size distribution

$m$: Parameter describing the spread of the distribution

The inverse distribution is given by:

$f(F;P_{\rm {80}},m)={\begin{cases}P_{\rm {80}}{\sqrt[{m}]{\frac {ln(1-F)}{ln(0.2)}}}&F>0,\\0&F\leq 0,\end{cases}}$

where

$F$: Mass fraction

Bibliography

• Fréchet, Maurice (1927), "Sur la loi de probabilité de l'écart maximum", Annales de la Société Polonaise de Mathematique, Cracovie, 6: 93–116.
• Rosin, P.; Rammler, E. (1933), "The Laws Governing the Fineness of Powdered Coal", Journal of the Institute of Fuel, 7: 29–36.