Hey @@Kashif Naukhez
To fit a power law distribution to your data points using Maximum Likelihood Estimation (MLE) in MATLAB, you can follow these steps:
1.Define the power law function powerLaw with parameters C and m:
powerLaw = @(C, m, E) C * E.^(-m);
2.Create a probability density function (PDF) of your data points E using the power law function:
pdf = @(C, m) powerLaw(C, m, E);
3.Define the negative log-likelihood function negLogLikelihood to be minimized:
negLogLikelihood = @(params) -sum(log(pdf(params(1), params(2))));
4.Use the fminsearch function to find the parameters C and m that minimize the negative log-likelihood:
initialGuess = [1, 1]; % Initial guess for C and m
params = fminsearch(negLogLikelihood, initialGuess);
C = params(1);
m = params(2);
5.Plot the data points E and the fitted power law curve:
scatter(E, P, 'b', 'filled');
hold on;
x = linspace(min(E), max(E), 100);
plot(x, powerLaw(C, m, x), 'r', 'LineWidth', 2);
xlabel('E');
ylabel('P(E)');
legend('Data', 'Power Law Fit');
Make sure to replace E and P with your actual data points and their corresponding probabilities.
