Main_TestHypothesis_IgGOF.m

%   Asymptotic Anderson-Darling Test for IG Distribution
%
%
%   GOAL :  Program runs Anderson-Darling Test on M random samples of N rvs, devised by Reilly and Rueda
%           (See "Goodness of Fit for Inv Gaussian Distbtn" by Federico J. O'Reilly and Raul Rueda
%           The Canadian Journal of Statistics, vol. 20, no. 4, pp. 387-397, 1992)
%
%   INPUT:
%       1)  Anderson Darling Critical Value as a function of Theta for given Alpha Level Test
%           Alpha values of 1%, 5%, and 10% can be specified by the user, along with necesary input files.
%       2)  N random samples of M rvs each (read in from file or generated)
%
%   FLOW:
%       1)  INITIALIZE BASIC PARAMS & ARRAYS
%           a)  Read in Table of Shape Values (log base2 of Theta = Lambda/Mu)
%           b)  Read in Critical Values for Chosen Value of Alpha to be used in hypothesis test
%           c)  Read in Data File containing M random samples (M) of rvs in each sample (N) to be tested
%               NOTICE THAT INPUT DATA MUST BE STRUCTURED SO IT IS AN MXN MATRIX
%       2)  RUN AD Test
%           a) Compute Mu,Lambda,and Theta (Shape Factor) for each Sample
%           b) Compute AD Test Statistic
%           c) Compute Critcal Value for given alpha level and compare to AD test statistic
%           d) decide to accept H0 if rejection rate < alpha
%       3)  Plot histogram of MLE for Theta from all random sample
%
%   OUTPUT
%       Percentage of times H0 rejected
%
%   PROGRAM TEST
%       This program can be tested by running the program using as the input file for the data to be tested
%       a control file called "CONTROL_1000RanSamples_Mu1_Lambda3_20RVs.dat", which is a file of 1000 random samples
%       each having 20 Ig RVs with Mu=1 and Lambda = 3.
%       SHOULD OBTAIN REJECTION RATE OF 8.9%
%
%   Written by M.T. Brenneman / Final Test on May 6th, 2009
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
clear all
close all
clc
%
global M N
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% STEP 1 : INITIALIZE BASIC PARAMS AND ARRAYS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%       a) Read in Shape values from file
TableShape = csvread('ShapeVals.dat');
%
%       b) SPECIFY ALPHA, then read in appropriate critical values from file
Alpha = 10;                                 %   Confidence Level of Test MUST BE SPECIFIED (Alpha = 1,5,10)
TableCV = Subr_InputCVs(Alpha);             %   Returns table of Critical Values for appropriate value of alpha
%
%   c) Read in Data 
G = csvread('UserSpecifiedInputFile.dat');                  %   Read data file
[M,N] = size(G);                            %   Determine number of ransom samples (M) and number of rvs/sample (N)
NumRejects = 0;                             %   Number of random samples for which H0 rejected a Alpha Confidence Level
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% STEP 2  :   RUN AD TEST  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%       a) COMPUTE MU, LAMBDA, AND SHAPE FACTOR FOR EACH RANDOM SAMPLE
[Mu,Lambda,Theta] = Subr_ComputeIgMLEParams(G);
%
%       B)  COMPUTE AD TEST STATISTIC FOR EACH RANDOM SAMPLE
[AD] = Subr_ComputeADTestStat(Mu,Lambda,G);
%
%       C)  TEST AD STAT AGAINST CRITICAL VALUE FOR GIVEN TYPE I ERROR CHOSEN
[CV] = Subr_ComputeCritVals(Theta,TableShape,TableCV,Alpha);               % Compute Critical Values from Table Using Log Interp
for ii = 1:M
    if AD(1,ii) > CV(1,ii)
        NumRejects = NumRejects + 1;
    end
end
%
%       D) Decide to Reject or Accept H_0
Pvalue = 100*NumRejects/M;
if Pvalue > Alpha
    disp(['Estimated Rejection rate = ' num2str(Pvalue) ' % > alpha level test at ' num2str(Alpha) ' %'])
    disp('Reject H_0 that random sample is from Inv Gaussian distribution')
else
    disp(['Estimated Rejection rate = ' num2str(Pvalue) ' % < alpha level test at ' num2str(Alpha) ' %'])
    disp('Accept H_0 that random sample is from Inv Gaussian distribution')
end
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   STEP 3  : OUTPUT RESULTS  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% subplot(3,1,1)
% hist(Mu)
% title(['\mu values with mean = ' num2str(mean(Mu)) ])
% subplot(3,1,2)
% hist(Lambda)
% title(['\lambda values with mean = ' num2str(mean(Lambda))])
% subplot(3,1,3)
% hist(CV)
% title(['Distbtn of Critical Values Producing P value = ' num2str(100*EstPvalue) ' % for \alpha = ' num2str(Alpha) ' =  %'])
% csvwrite('CV_10KRanSamp_16SideBands.dat',CV)