MATLAB: Fitting Cumulative Gaussian Function to Data Points

cumulative functions

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 🙂

Best Answer

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
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