bpafromdata {ipptoolbox}R Documentation

Generating BPAs from point / interval data

Description

A set of functions to create empirical BPAs from data sets (either points or intervals).

Usage

dsecdffit(x)
dslapconf(x, lims = c(-Inf, Inf))
dsksconf(x, conf = 0.95, lims = c(-Inf, Inf))

Arguments

x Array of points / matrix with interval data
lims Optional: Limits of the BPA for cutting first and last focal elements.
conf Confidence level of Kolmogorov-Smirnov fit in ]0,1[.

Details

dsecdffit
Creates a BPA of the data set analoguous to probabilistic empirical CDF
dslapconf
Creates a BPA of the data set according to the Laplace method
dsksconf
Creates a BPA of the data set from the Kolmogorov-Smirnov bounds for a given confidence.

The toolbox contains a set of functions to create empirical BPAs from data sets. These data sets may be either standard data values or intervals (e.g. caused by measurement imprecision). dsecdffit creates a BPA of the data set analogous to probabilistic empirical CDF. It is not conservative respective to distribution tails. dslapconf creates a BPA according to the Laplace method, dsksconf from the Kolmogorov-Smirnov bounds for a given confidence.

The example illustrates the three different methods on interval and point data. First, 20 random values and intervals are generated. Then, dsecdffit, dslapconf and dsksconf are used to generate fits for both data sets.

Value

BPA according to the chosen method.

Author(s)

Philipp Limbourg <p.limbourg@uni-due.de>

References

Ferson, S., V. Kreinovich, et al. (2003). Constructing Probability Boxes and Dempster-Shafer Structures. Sandia Report. Albuquerque, USA, Sandia National Laboratories.

Examples

print("Create random data sets")
setofpoints=rnorm(20,0,1)
setofintervals=cbind(setofpoints-runif(20,0,1),setofpoints+runif(20,0,1))
print("Plot ecdf for both points and interval data")
ecdfp=dsecdffit(setofpoints)
dscdf(ecdfp)

ecdfi=dsecdffit(setofintervals)
dscdf(ecdfi)

print("Plot Laplace BPA for both points and interval data")
lapp=dslapconf(setofpoints,lim=c(-5,5))
dscdf(lapp)

lapi=dslapconf(setofintervals,lim=c(-5,5))
dscdf(lapi)

print("Plot Kolmogorov-Smirnov 75 percent bound BPA for both points and interval data")

ksp=dsksconf(setofpoints,conf=0.75,lim=c(-5,5))
dscdf(ksp)

ksi=dsksconf(setofintervals,conf=0.75,lim=c(-5,5))
dscdf(ksi)

[Package ipptoolbox version 1.0 Index]