Fitting Cumulative Gaussian Function to Data Points

Hello,

I am trying to fit the cumulative Gaussian Function to my data points, to find out the PSE. So far I used this function:

 f = @(b,x_values) normcdf(x_values, b(1), b(2));          % Objective Function
    NRCF = @(b) norm(yVorB - f(b,x_values));     % Norm Residual Cost Function
    B1 = fminsearch(NRCF, [-1; 5]);               % Estimate Parameters

x = 0:5
y = [0.7 0.4 0.2 0.4 0.6 0.9]

I am getting: 1.81051

However, the correct value should be: 1.91293286. Does anyone have ideas? Is there a better way to fit the cumulative function to my data in Matlab?

Thank you for your help :)

Answer 1

[Matt J]

Your data points don't look anything like a CDF to me (no monotonic trend of any kind), but one of the estimated parameter values I get is pretty close to what you say you're looking for.

format long

x = 0:5;
y = [0.7 0.4 0.2 0.4 0.6 0.9];

     f = @(b,x_values) normcdf(x_values, b(1), b(2));          % Objective Function
    NRCF = @(b) norm(y - f(b,x));     % Norm Residual Cost Function
params = fminsearch(NRCF, [-1; 5])               % Estimate Parameters

params = 2×1

1.912932525139948 7.839459850514324

[TS]

Hey,

thank you for your quick answer! Sorry, I just saw that I am getting 1.91, however the correct answer is 1.81. Sorry, I messed them up.

Because I used the same way as you to figure out PSE so far. You did not change anything in the function, if I am correct?

[Matt J]

My definition of NRCF is different from yours. It uses y and x instead of yVorB and x_values.