CodeCogs

Rosin-Rammler cumulative distribution

Interface

#include <codecogs/statistics/distributions/continuous/rosin_rammler.h>

using namespace Statistics::Distributions::Continuous;

double Rosin_CDF(double Dm, int n, double D)

The Rosin-Rammler distribution is frequently used to describe the particle size distribution of powers of various types and sizes. The function is particularyly suited to representing particles generated by grinding, milling and crushing operations. The conventional Rosin-Rammler function is described by

$R = exp \left [ - \left ( \frac{D}{D_m} \right )^n \right ]$

(1)

where R is the retained weight fraction of particles with a diameter greater than D, D is the particle size and $D_m$ is the mean particle size, and n is a measure of the spread of particle sizes.

The Cumulative Distribution Function (CDF) is therefore

$R_{cdf} = 1- exp \left [ - \left ( \frac{D}{D_m} \right )^n \right ]$

(2)

As an additional note, the PDF is:

$R_{pdf} = -\frac{n}{D} \left ( \frac{D}{D_m} \right )^n exp \left [- \left( \frac{D}{D_m} \right )^n \right ]$

(3)

\graph Dm=0.1e-3 n=2 D=0:0.3e-3

If you have observed data, then a least square regression analysis can used to fit the data points.

Parameters

mean particle diameter

measure of the spread of particle sizes

particle size

References

K.M. Djamarani and I.M. Clark, 1997. Powder Technology, Elsevier Science. 93, No 2, pp. 101-108(8)

Interactive Calculator

Result –

Rosin_Rammler

Interface

Parameters

References