function KLDistanceAndLikelihoodFuction = SingleCluster(N1,N2,Shift1,Shift2);

X1 = randn(N1,1)+Shift1;       %Generate the first normal distribution with prior N1/(N1+N2) and mean at Shift1;

X2 = randn(N2,1)+Shift2;       %Generate the second normal distribution with prior N2/(N1+N2) and mean at Shift2;

Xaxis = -10:0.01:10;

subplot(2,2,1);  hist(X1); title('Input data set 1');

subplot(2,2,2);  hist(X2); title('Input data set 2');

meanX1 = mean(X1);

meanX2 = mean(X2);

covX1 = cov(X1);

covX2= cov(X2);          %Calculate the mean and covariance of both sets of data

X3 = [X1,
      X2] ;              %Combine the two sets of data

meanX3 = mean(X3);       %Calculate the mean of the combined data

covX3 = cov(X3);         %Calculate the covariance of the combined data

P =0.4*(1/((2*pi*abs(covX1))^0.5))*exp(-0.5*covX1^-1*(Xaxis-meanX1).*(Xaxis-meanX1))+0.6*(1/((2*pi*abs(covX2))^0.5))*exp(-0.5*covX2^-1*(Xaxis-meanX2).*(Xaxis-meanX2));                     

                          %Calculate the input sets distribution

subplot(2,2,3);  

scatter(Xaxis,P);   title('Input data distribution');      


P1 = (1/((2*pi*abs(covX3))^0.5))*exp(-0.5*covX3^-1*(Xaxis-meanX3).*(Xaxis-meanX3));

                         %Estimate the combined data by one Gaussian distribution

subplot(2,2,4);

scatter(Xaxis,P1);  title('Single Gaussian Cluster Estimation');       

D= sum(P1.*log(P1./P));   %Calculate the KL distance 

L = sum(log(P1));         %Calculate the log-Likelihood function value

fprintf( 'The Value of KL Distance is %g.\n',D);
fprintf( 'The Value of log likelihood fuction is %g.\n',L);