To include confidence intervals in a Q-Q plot for a distribution fit, you can follow these steps. MATLAB's qqplot function doesn't natively support confidence intervals directly, so you'll have to calculate and plot them manually. Here’s a conceptual approach to achieve this:
- Generate your sample data from the distribution.
- Perform the Q-Q plot using qqplot.
- Calculate theoretical quantiles for the desired confidence intervals from the distribution.
- Calculate empirical quantiles from your sample data.
- Plot confidence intervals around the theoretical quantiles on the Q-Q plot.
Here's how you can implement it with a Rician distribution example:
% Generate sample data
pd1 = makedist('Rician', 's', 1, 'sigma', 1);
sampleData = random(pd1,1e3,1);
% Perform the Q-Q plot
figure(1);
qqplot(sampleData, pd1);
% Calculate theoretical and empirical quantiles
p = (0.5:999.5)/1000; % Adjust the range based on your sample size
theoreticalQuantiles = icdf(pd1, p);
empiricalQuantiles = quantile(sampleData, p);
% Calculate confidence intervals for the theoretical quantiles
% This is a simple approach for demonstration; for actual confidence intervals,
% you may need a more specific method depending on the distribution and the data.
ci = 1.96 * std(sampleData) / sqrt(length(sampleData)); % 95% CI assuming normality
lowerBound = theoreticalQuantiles - ci;
upperBound = theoreticalQuantiles + ci;
% Plot confidence intervals
hold on;
plot(lowerBound, empiricalQuantiles, 'r--'); % Lower CI
plot(upperBound, empiricalQuantiles, 'r--'); % Upper CI
hold off;
This example uses a basic approach for calculating and plotting confidence intervals, assuming normality for simplicity and using 1.96 as the z-value for a 95% confidence interval. The confidence intervals are plotted as dashed red lines around the theoretical quantiles.
Note: The accuracy of these confidence intervals depends on the distribution of your data and the assumptions you're willing to make. For non-normal distributions or more accurate CI calculations, you might need to employ distribution-specific methods or bootstrapping techniques.
