Area under distribution fit curve

I used Statistics and Machine Learning add on to help me create a fit for my data. However, i now need to find the area under the fitted curve, and i am unable to use trapz(X,Y) since i do not have any variables and my data is a 261345x1 data set. Please advise!

Answer 1

[Star Strider]

It would help to know the function used to fit the curve (for example nlinfit).

The nonlinear curve-fitting functions require that a model function be provided in order to estimate the parameters. That function can then be used with the integral function to find the area under the fitted curve, or to calculate the fitted values to use with trapz —

t = linspace(0, 5);
s = t.^2 + randn(size(t));

fcn = @(b,x) b(1) .* x.^b(2);
B0 = rand(2,1);
B = nlinfit(t, s, fcn ,B0)

B = 2×1

0.9334 2.0407

AUC1 = integral(@(x)fcn(B,x), min(t), max(t))                           % Use 'integral'

AUC1 = 40.9677

AUC2 = trapz(t, fcn(B,t))                                               % Use 'trapz'

AUC2 = 40.9699

figure
plot(t, s, '.')
hold on
plot(t, fcn(B,t), '-r')
hold off
grid

Experiment to get different results.

.

Answer 2

[KSSV]

Let Y be your 261345x1 data.

X = (1:length(Y))' ; 
trapz(X,Y)