Fit T2 distribution with 2 gaussian distributions

Today, I successfully fitted T2 distribution with 2 gaussian distributions.

Summary:

%% fit T2 with gaussian distribution
% b(1) is scale, b(2) is sigma, b(3) is miu.
modelfun1=@(b,x)(b(1)*(1/(b(2)*sqrt(2 * pi))) * exp(-(x - b(3)).^2 ./ (2 * b(2)^2)));
x1=(1:40);
y1=T2row1(:,(1:40));
x2=(40:64);
y2=T2row1(:,(40:64));
beta10=[0.01;1;10];
beta20=[0.01;1;50];
beta1=nlinfit(x1,y1,modelfun1,beta10);
beta2=nlinfit(x2,y2,modelfun1,beta20);
[beta1,R1,J1,CovB1,MSE1,ErrorModelInfo1]=nlinfit(x1,y1,modelfun1,beta10);
[beta2,R2,J2,CovB2,MSE2,ErrorModelInfo2]=nlinfit(x2,y2,modelfun1,beta20);
fun1=beta1(1,:)*(1/(beta1(2,:)*sqrt(2 * pi))) * exp(-(x1 - beta1(3,:)).^2 ./ (2 * beta1(2,:)^2));
fun2=beta2(1,:)*(1/(beta2(2,:)*sqrt(2 * pi))) * exp(-(x2 - beta2(3,:)).^2 ./ (2 * beta2(2,:)^2));

%% plot
hold off;
plot(T2row1)
hold on;
plot(x1,fun1, 'r-');
plot(x2,fun2, 'r-');
title('T2 distribution fitting');
rsq1=1-sum(R1.^2)/sum((y1-mean(y1)).^2)
rsq2=1-sum(R2.^2)/sum((y2-mean(y2)).^2)

Result:

beta1 =

    0.0426
    6.5562
   19.3092

beta2 =

    0.0042
    2.6393
   49.9026

The first is the scale to adjust gaussian distribution, the second is standard deviation, the third is mean value. I calculated that the r square for the first gaussian distribution is 0.9695 and  the r square for the second gaussian distribution is 0.9907. Both of them are good enough for fitting.

Next week, I will try to apply the method to all the depth of T2 distribution.