Value of x for which AUC reaches a given value

Hello,

I need to find the point on the x axis where the AUC of a given curve reaches 50% of its value.

I calculate the AUC using the trapz function. I guess at this point I need a reverse formula to find the value of x there the AUC reaches a given value.

Could anybody please help me with that formula?

Answer 1

[Star Strider]

‘I calculate the AUC using the trapz function.’

That being the problem. Use cumtrapz instead:

t = linspace(0, 1, 500);                        % Create Data
x = rand(size(t));                             % Create Data

AUC = cumtrapz(t,x);
AUC50 = interp1(AUC, t, AUC(end)/2);

figure
plot(t, AUC)
hold on
plot(AUC50, AUC(end)/2, 'p')
hold off
text(AUC50, AUC(end)/2, sprintf('\\leftarrow AUC = %.2f at %.2f', AUC(end)/2, AUC50), 'HorizontalAlignment','left', 'VerticalAlignment','middle')

.

[Alessandra Piatti]

Thank you very much! This spared me a lot of banging my head against the wall!

[Star Strider]

As always, my pleasure!

(That sounds painful! Don’t do it!)