fitDRC-package: Fitting Density Ratio Classes

In fitDRC: Fitting Density Ratio Classes

Description

Constructs the smallest Density Ratio Class for elicited probability-quantile points (or intervals) given a lower and upper distributional shape. Used optimisation algorithms are the methods Nelder-Mead and L-BFGS-B implemented in the standard R function optim. The package is easily customizable by using templates from the example section for distributions and transformations that are not implemented yet.

Details

Package:	fitDRC
Type:	Package
Version:	1.1.1
Date:	2018-06-08
License:	GPL-2
LazyLoad:	yes

The most important functions producing objects or results are:

(1) dist.distributionfamily.create(...)	see for the class description distribution
(2) trans.transformationkind.create(...)	see for the class description transformation
(3) dist.trans.create(...)	see for the constructor description dist.trans.create
(4) process.elidat(...)	see for the processing description process.elidat

(1) creates an object of the class distribution that is used to design lower and upper distribution of the Density Ratio Class whereby the implemented distributions are:

Normal	dist.normal.create
Student	dist.student.create
Weibull	dist.weibull.create
Lognormal	dist.lognormal.create
Beta	dist.beta.create
Gamma	dist.gamma.create
F	dist.f.create
Uniform	dist.uniform.create
Logistic	dist.logistic.create

(2) creates an object of the class transformation that is used to transform the distribution(s) with (3) (see dist.trans.create) returning again an object of the class distribution. However, implemented transformations are:

Arctan	trans.arctan.create
Tan	trans.tan.create
Log	trans.log.create
Exponential	trans.exp.create
Dilation	trans.dil.create

(4) processes the probability-quantile intervals/points in combination with the lower and upper distribution and returns an object of the class drclass that is the Density Ratio Class one wants to obtain (see process.elidat). Several methods are implemented for each class described above. Use the templates from the example sections for the implementation of distributions and transformations that are not implemented yet.

Author(s)

Simon L. Rinderknecht and Peter Reichert.

References

Rinderknecht, S.L., Borsuk, M.E. and Reichert, P. Eliciting Density Ratio Classes. International Journal of Approximate Reasoning 52, 792-804, 2011. doi10.1016/j.ijar.2011.02.002. \ Rinderknecht, S. L., Borsuk, M. E. and Reichert, P. Bridging Uncertain and Ambiguous Knowledge with Imprecise Probabilities, Environmental Modelling & Software 36, 122-130, 2012.

Examples

################# Example 01 ################

# Demonstration of the construction of a very narrow Density Ratio Class
# for a case where the input quantiles correspond to the quantiles of the
# parametric distribution used for the lower and upper densities (in this
# case both are Normal distributions).

# Definition of quantiles:

p <- c(0.05, 0.25, 0.5, 0.75, 0.95)
q <- qnorm(p)

# Definition of parametric shapes of lower and upper densities (Normal):

dist.lower <- dist.normal.create(par=c(1,2))
dist.upper <- dist.normal.create(par=c(3,4))

# Parameter estimation (attention: runtime several minutes):

#res <- process.elidat(p = p,
#                      q = q,
#                      dist.lower,
#                      dist.upper,
#                      start.dist.lower.par = c("Mean"=2,"StDev"=3),
#                      start.dist.upper.par = c("Mean"=4,"StDev"=5))

# Extract density ratio class, print and plot results:

#drc01 <- res$drc
#print(drc01)
#plot(drc01)

################# Example 02 ################

# Demonstration of the construction of a Density Ratio Class using tans-
# formed beta distributions for lower and upper densities.

# Definition of quantiles:

p <- c(0.05, 0.25, 0.5, 0.75, 0.95)
q <- c(80, 145, 200, 240, 280)

# Definition of parametric shapes of lower and upper densities (transf. beta):

dist.beta  <- dist.beta.create(par=c(2.5,2.5))
trans.dil <- trans.dil.create(c(60, 305, 0, 1))

dist.lower <- dist.trans.create(dist.beta,trans.dil)
dist.upper <- dist.lower

# Parameter estimation (attention: runtime several minutes):

#res <- process.elidat(p = p,
#                      q = q,
#                      dist.lower,
#                      dist.upper,
#                      start.dist.lower.par =c("Shape1"=2.5,"Shape2"=2.5),
#                      start.dist.upper.par = c("Shape1"=2.5,"Shape2"=2.5))

# Extract density ratio class, print and plot results:

#drc02 <- res$drc
#print(drc02)
#plot(drc02)

# Note, due to the transformation, mean, standard deviation, median and mode
# cannot be calculated analytically (print(drc02 returns NA)). However, these
# characteristics can be calculated  numerically, using a sample from the
# distribution (demonstrated for the lower density):

# Mean:
#mean(CDFinv(drc02$dist.lower,runif(100000,0,1),drc02$dist.lower$par))

# Standard Deviation:
#sd(CDFinv(drc02$dist.lower,runif(100000,0,1),drc02$dist.lower$par))

# Median:
#CDFinv(drc02$dist.lower,0.5)

# Mode:
#samp <- runif(100000,0,1)
#ind.max <- which.max(PDF(drc02$dist.lower,
#                         CDFinv(drc02$dist.lower,samp,drc02$dist.lower$par),
#                         drc02$dist.lower$par))
#CDFinv(drc02$dist.lower,samp[ind.max],drc02$dist.lower$par)

################# Example 03 ################

# Demonstration of the construction of a Density Ratio Class using different
# parametric shapes for lower (Normal) and upper (Student t) distributions.

# Definition of quantiles:

p <- c(0.05, 0.25, 0.5, 0.75, 0.95, 0.05, 0.25, 0.5, 0.75, 0.95)
q <- log(c(1, 2, 4, 6, 10, 2, 3, 5, 9, 14))

# Definition of parametric shapes of lower and upper densities (Normal and
# Student t):

dist.lower <- dist.normal.create(par=c(1,1))
dist.upper <- dist.student.create(par=c(1,1,3))

# Parameter estimation (attention: runtime several minutes):

#res <- process.elidat(p = p,
#                      q = q,
#                      dist.lower,
#                      dist.upper,
#                      start.dist.lower.par = c("Mean"=1,"StDev"=1),
#                      start.dist.upper.par = c("Mean"=1,"StDev"=1))

# Extract density ratio class, print and plot results:

#drc03 <- res$drc
#print(drc03)
#plot(drc03,range=c(0.001,15))

fitDRC documentation built on May 2, 2019, 3:29 a.m.