How to extract fitted data from normal probability density function

Question

If I fit a uni-variate data with normal distribution, how can i get back the fitted values in MATLAB. I am using this simple example

load hospital % data
x = hospital.Weight;
[mu sigma]=normfit(x) %normal fitting
%To visualize the pdf
xval=min(x):0.1:max(x)
yval=normpdf(xval,mu,sigma)
plot(xval,yval)

yval is giving the probabilities of xval values. Now, If I would like to extract the fitted values of 'x' after approximating it with the above normal distribution, how do I do that?. As can be seen in the picture the y-axis values are the pdf and lies between 0 and 1, however I want the corresponding fitted values from the data that follows normal distribution.

Would the fitted values be x_fitted = yval*sigma + mu? !I think I am missing some basic maths here.

Answer 1

normfit simply gives you the mu and sigma of the fitted normal pdf. From those you build that pdf with normpdf. So the desired y values for your input x would be

y = normpdf(x,mu,sigma)

which you could plot with

hold on
plot(x,y,'ro')

Note that, with this procedure, the data lie exactly on the normal pdf, even if those data do not actually follow a normal distribution.