Fitting Cumulative Normal Distribution Function to Data

Hello, I have the following data and would like to fit a cumulative normal distribution to it.

X = [-75, -50, -17, -9, 11, 25, 43, 67]; Y = [5, 0, 25, 25, 65, 80, 70, 75];

By dividing by 100, these values can be normalized such that X goes from -1 to 1 and Y goes from 0 to 1.

I'd like to fit this data so that the error is minimized between my recorded Y values and the values of an appropriate cumulative normal distribution function. How can I determine the values for Mu and Sigma? I tried using normfit, but that only used my X values and nothing changed when my data changed.

I'd also like to get an R-squared metric for the goodness of fit if possible.

Thanks in advance, Jake

Answer 1

[Star Strider]

This seems to work:

X = [-75, -50, -17, -9, 11, 25, 43, 67];
Y = [5, 0, 25, 25, 65, 80, 70, 75];

fcn = @(b,x) normcdf(x, b(1), b(2));                    % Objective Function

NRCF = @(b) norm(Y/100 - fcn(b,X));                     % Norm Residual Cost Function
B = fminsearch(NRCF, [0; 10]);                          % Estimate Parameters

Xplot = linspace(min(X), max(X));

figure(1)
plot(X, Y/100, 'pg')
hold on
plot(Xplot, fcn(B,Xplot))
hold off
grid
text(-50, 0.65, sprintf('\\mu = %.1f\n\\sigma = %.1f', B))

[linlin]

Hello,I want to make a cumulative chi-square distribution fitting data. How do I rewrite the program? After I rewrite it, it has been unable to fit.

[linlin]

May I ask the first half of the fitting effect is not very good, what measures should be taken?

[Star Strider]

It is apparently not the correct distribution for those data.

[linlin]

Then how should I fit it, thank you

[linlin]

I just started to learn this and I still don’t understand, can you help me, thank you

[linlin]

X = [38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64];

Y = [0 0.02 0.02 0.03 0.04 0.04 0.05 0.05 0.07 0.08 0.08 0.08 0.1 0.11 0.14 0.17 0.19 0.2 0.25 0.44 0.51 0.6 0.67 0.78 0.87 0.96 1];

The data I want to fit is this.

[linlin]

When x is less than 38, y is all 0; when x is greater than 64, y is all 1. So it should obey the cdf distribution

[Star Strider]

truncate

[linlin]

I don't understand, can you tell me more specifically. Scientific research novice, trouble

[linlin]

And my data is CDF, not PDF

[linlin]

This seems to be a worse fit, please give pointers, thank you

[linlin]

Can you give me some pointers?

[Rohit Sinha]

@Star Strider I tried using your function, however, the starting values of probability even though are zero, or approximately zero, there is a slight difference in the initial point of the fitted curve as shown