I have some archive code that can help you get started.
If you want to fit what is essentially a histogram to the normal distribution, here is one way:
% Generate x- and y- data:
x = linspace(0,10);
% Normal distribution — b(1) = mean, b(2) = std
N = @(b,x) exp(-((x-b(1)).^2)./(2*b(2)^2)) ./ (b(2)*sqrt(2*pi));
b = [5; 1];
d1 = N(b,x); % Generate smooth data
d2 = d1 + 0.05*(rand(size(d1))-.5); % Add noise
% Use ‘fminsearch’ to do regression:
y = d2;
OLS = @(b) sum((N(b,x) - y).^2); % Ordinary Least Squares cost function
opts4 = optimset('MaxFunEvals',50000, 'MaxIter',10000);
B = fminsearch(OLS, rand(2,1))
Nfit = N(B,x);
figure(1)
plot(x, d1, '-b')
hold on
plot(x, d2, '.g')
plot(x, Nfit, '-r')
hold off
grid
I’ll let you experiment with it. Change the initial estimate for the mean to fit other peaks in your data.
With regard to the patch colouring, another bit of archived code will provide an example:
alpha = 0.05; % significance level
mu = 82.9; % mean
sigma = 8.698; % std
x = linspace(mu-5*sigma, mu+5*sigma, 500);
cutoff1 = norminv(alpha/2, mu, sigma); % Lower 95% CI is p = 0.025
cutoff2 = norminv(1-alpha/2, mu, sigma); % Upper 95% CI is p = 0.975
y = normpdf(x, mu, sigma);—
xci = [linspace(mu-5*sigma, cutoff1); linspace(cutoff2, mu+5*sigma)];
yci = normpdf(xci, mu, sigma);
figure(1)
plot(x, y, '-b', 'LineWidth', 1.5)
patch(x, y, [0.5 0.5 0.5])
patch([xci(1,:) cutoff1], [yci(1,:) 0], [1 1 1])
patch([cutoff2 xci(2,:)], [0 yci(2,:)], [1 1 1])
This shades the 95% confidence intervals, but it easily adapted to do what you want.
