ipptoolbox (version 1.2)

bpafromdata: 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[.

Value

BPA according to the chosen method.

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.

References

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

Examples

# NOT RUN {
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)
# }