Rebuild PDFs from original data

Hello,

I have two histograms for two classes data (class1 and class2) and I want to create for each class a Chi2 distribution that represents the original data.

So how and what I should extract from the original data (mean, std, variance, ......) to build my two Chi2 distributions ?

Thanks.

load('data.mat')
histogram(class1)
hold on
histogram(class2)

Answer 1

[Star Strider]

The is not an option for histfit or the others, however calculating the parameters is straightforward —

LD = load('data.mat');
class1 = LD.class1;
class2 = LD.class2;

figure
subplot(2,1,1)
histogram(class1,1000, 'DisplayStyle','stairs')
xlabel('Bin')
ylabel('Count')
xlim([0 1])
title('Class 1')
[muest1,sdest1] = normfit(class1);
text(0.5,max(ylim), sprintf('\\mu = %.3f\n\\sigma = %.3f',muest1,sdest1), 'Horiz','left', 'Vert','top')
grid
subplot(2,1,2)
histogram(class2,1000, 'DisplayStyle','stairs')
xlabel('Bin')
ylabel('Count')
xlim([0 1])
title('Class 2')
[muest2,sdest2] = normfit(class2);
text(0.5,max(ylim), sprintf('\\mu = %.3f\n\\sigma = %.3f',muest2,sdest2), 'Horiz','left', 'Vert','top')
grid

.

[Khoder Makkawi]

Thanks for this explanation. However, what I want is to approximate these two distributions with a Chi2 distributions. So I don't want to use normfit, I want to recreate a Chi2 that approximates each distribution. So if I extract the mean for example, can I approximate it with this ?:

rng = -10:0.1:10;
class1 = pdf('Chisquare',rng,muest1);
class2 = pdf('Chisquare',rng,muest2);

[Star Strider]

This is the best I can do with your data —

figure
subplot(2,1,1)
[h1,stats1] = cdfplot(class1);
xv1 = h1.XData(isfinite(h1.XData));
yv1 = h1.YData(isfinite(h1.XData));
nu1 = fminsearch(@(nu) norm(yv1 - chi2cdf(xv1,nu)), 1);
hold on
[muest1,sdest1] = normfit(class1);
class1cdf = cdf('Chisquare',xv1,nu1);
plot(xv1,class1cdf,'-r', 'LineWidth',1)
hold off
xlabel('x')
ylabel('cdf')
xlim([0 1])
title('Class 1')
text(0.01,max(ylim), sprintf('\\nu = %.3f',nu1), 'Horiz','left', 'Vert','top')
legend('Empirical CDF',' \chi^2 Fit', 'Location','best')
grid
subplot(2,1,2)
[h2,stats2] = cdfplot(class2);
xv2 = h2.XData(isfinite(h2.XData));
yv2 = h2.YData(isfinite(h2.XData));
nu2 = fminsearch(@(nu) norm(yv2 - chi2cdf(xv2,nu)), 1);
hold on
class1cdf = cdf('Chisquare',xv2,nu2);
plot(xv2,class1cdf,'-r', 'LineWidth',1)
hold off
xlabel('x')
ylabel('cdf')
xlim([0 1])
title('Class 2')
text(0.01,max(ylim), sprintf('\\nu = %.3f',nu2), 'Horiz','left', 'Vert','top')
legend('Empirical CDF',' \chi^2 Fit', 'Location','best')
grid

.

[Jeff Miller]

These data don't seem to come from any chi^2 distribution. The mean of a chi^2 equals its degrees of freedom, which is at least 1. These data sets have means far less than 1, so that is simply incompatible with any chi^2.

[Star Strider]

@Jeff Miller — I agree. I was also not aware that data were ever -distributed, only that parameters were.