Rosin - Rammler model of particle-size distribution and cumulative undersize and oversize distributions used to obtain approximation of of powders or granular materials originated by grinding.

1 2 3 |

`x` |
particle size, equivalent particle diameter |

`ex` |
Rosin - Rammler exponent, measure of the uniformity of grinding |

`xs` |
finesse of grinding, that width of mesh associated with a remainder
equal to |

Following functions are used, based on Rosin - Rammler mathematical model of particle-size distribution, for approximation of size distribution.

`drr`

is Rosin - Rammler probability density function

`urr`

is Rosin - Rammler cumulative distribution function (CDF) representing undersize mass fraction

`orr`

is Rosin - Rammler complementary CDF representing oversize mass fraction ie. relative remainder on the sieve with the mesh size `x`

Rosin - Rammler model (1933) is the Weibull distribution which was proposed by Weibull in 1939, and Weibull distribution functions are part of **R**.

So the user can use `stats::dweibull(x,shape=ex,scale=xs)`

the same way as `drr`

,
and use Weibull distribution functions provided by `stats`

package for deeper analysis.

Similarly, `stats::pweibull(x,shape=ex,scale=xs)`

can be used the same way as `urr`

or

`stats::pweibull(x,shape=ex,scale=xs,lower.tail=F)`

the same way as `orr`

.

Both `urr`

and `orr`

returns value of distribution function.

Function `drr`

returns density.

Rinne, H. (2008) *The Weibull Distribution: A Handbook*, chapter 1.1.2. Taylor & Francis.

`Weibull`

, `plot.std`

, `summary.std`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | ```
## The function drr is currently defined as
# function (x, ex, xs)
# {
# (ex/xs) * (x/xs)^(ex - 1) * exp(-(x/xs)^ex)
# }
## The function urr is currently defined as
# function (x, ex, xs)
# {
# 1 - exp(-(x/xs)^ex)
# }
## The function orr is currently defined as
# function (x, ex, xs)
# {
# exp(-(x/xs)^ex)
# }
x <- c(1,5,10,50,100)
ex <- 1.386
xs <- 178
stats::dweibull(x,shape=ex,scale=xs)
drr(x,ex,xs)
stats::pweibull(x,shape=ex,scale=xs)
urr(x,ex,xs)
stats::pweibull(x,shape=ex,scale=xs,lower.tail=FALSE)
orr(x,ex,xs)
``` |

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