Description Usage Arguments Details Value References See Also Examples
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)
|
[1] 0.001052812 0.001947203 0.002515657 0.004015661 0.003975403
[1] 0.001052812 0.001947203 0.002515657 0.004015661 0.003975403
[1] 0.0007598937 0.0070494465 0.0183193131 0.1580748078 0.3621772219
[1] 0.0007598937 0.0070494465 0.0183193131 0.1580748078 0.3621772219
[1] 0.9992401 0.9929506 0.9816807 0.8419252 0.6378228
[1] 0.9992401 0.9929506 0.9816807 0.8419252 0.6378228
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