drr {sievetest} | R Documentation |
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.
drr(x, ex, xs)
orr(x, ex, xs)
urr(x, ex, xs)
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
## 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)