DigitFD

DigitFD generates random sample from the fiducial distribution of the parameters mu and sigma based

DigitFD generates random sample from the fiducial distribution of the parameters mu and sigma [of the unobservable normal distribution], based on the (digitized) measurements from instrument with limited, however known resolution. Here,

measurements = round( (mu + sigma * Z)/resolution ) * resolution,

where Z is an unobservable vector of independent standard normal errors.

Based on this Fiducial Distribution,
DigitFD estimates the confidence intervals for the parameter mu and sigma.

Syntax:
result = DigitFD(measurements)
result = DigitFD(measurements,options)

INPUTS:
measurements - vector of the digitized measurements;
options - options structure

OUTPUT:
result - results structure with the fields:
Resolution
Measurements
MeanMeasurements
StdMeasurements
NumberOfMeasurements
NumberOfDifferentValuesInMeasurements
CriticalNumberOfDifferentValuesInMeasurements
FiducialSample
FiducialSampleSize
FiducialConfidenceIntervalForMu
FiducialConfidenceIntervalForSigma
FiducialConfidenceIntervalForMuAdjusted
FiducialConfidenceIntervalForSigmaAdjusted
NominalSignificanceLevelAlpha
FastMethod
SamplingMethod
options

EXAMPLE 1 (Measurements with 2 different values)

figure
measurements =[zeros(10,1);ones(5,1)];
result = DigitFD(measurements)

EXAMPLE 2 (Micrometer measurements with resolution 0.001)

micrometer =[7.489; 7.503; 7.433; 7.549; 7.526; 7.396; ...
7.543; 7.509; 7.504; 7.383];
options = DigitFD;
options.resolution = 0.001;
subplot(1,2,1)
result1 = DigitFD(micrometer,options)
axis([7.35, 7.65, 0, 0.25])
axis('square')
title('Sample From Fiducial Distribution of (\mu,\sigma) - Fast FD Method')
options.isFast = false;
subplot(1,2,2)
result2 = DigitFD(micrometer,options)
axis([7.35, 7.65, 0, 0.25])
axis('square')
title('Sample From Fiducial Distribution of (\mu,\sigma) - Full FD Method')

References:
[1] Witkovsky V. and Wimmer G.: Confidence intervals for the location parameter based on digitized measurements. Mathematica Slovaca 2008, Submitted.

[2] Hannig J., Iyer H.K., and Wang C.M.: Fiducial approach to uncertainty
assessment accounting for error due to instrument resolution.
Metrologia, 44 (2007), 476–483. doi:10.1088/0026-1394/44/6/006.

Viktor Witkovsky ([e-mail])
Revised: 21-May-2008 08:58:08