DigitFD 1.0

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 structureOUTPUT:result - results structure with the fields: Resolution Measurements MeanMeasurements StdMeasurements NumberOfMeasurements NumberOfDifferentValuesInMeasurements CriticalNumberOfDifferentValuesInMeasurements FiducialSample FiducialSampleSize FiducialConfidenceIntervalForMu FiducialConfidenceIntervalForSigma FiducialConfidenceIntervalForMuAdjusted FiducialConfidenceIntervalForSigmaAdjusted NominalSignificanceLevelAlpha FastMethod SamplingMethod optionsEXAMPLE 1 (Measurements with 2 different values)figuremeasurements =[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), 476d-deOCt483. doi:10.1088/0026-1394/44/6/006.

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	3d7489,  Axis,  Axis Square,  Digitfdmicrometeroptions,  Micrometer,  Optionsresolution,  Result,  Subplot,  Title Sample
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