# drr: Rosin - Rammler Distribution Functions In sievetest: Laboratory Sieve Test Reporting Functions

## Description

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.

## Usage

 ```1 2 3``` ```drr(x, ex, xs) orr(x, ex, xs) urr(x, ex, xs) ```

## Arguments

 `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 `exp(-1) ~ 0.3679`

## Details

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`.

## Value

Both `urr` and `orr` returns value of distribution function.
Function `drr` returns density.

## References

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) ```