## DigitFD

version 1.0.0.0 (3.39 MB) by
DigitFD generates random sample from the fiducial distribution of the parameters mu and sigma based

Updated 21 May 2008

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
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 (witkovsky@savba.sk)
Revised: 21-May-2008 08:58:08

### Cite As

Viktor Witkovsky (2022). DigitFD (https://www.mathworks.com/matlabcentral/fileexchange/19802-digitfd), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2006b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux