User:Dhatfield/Sandbox Rosin-Rammler distribution

Rosin-Rammler distribution
The Weibull distribution, now named for Waloddi Weibull was first identified by and first applied by  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\geq0 ,\\ 0 & x<0 ,\end{cases}$$ where
 * $$x$$: Particle size
 * $$P_{\rm{80}}$$: 80th percentile of the particle size distribution
 * $$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\leq0 ,\end{cases}$$

where
 * $$F$$: Mass fraction