I'm having problems in curve fitting my randomized data for the function

Here is my code

N = 100;
mu = 5; stdev = 2;
x = mu stdev*randn(N,1);
bin=mu-6*stdev:0.5:mu 6*stdev;
f=hist(x,bin);
plot(bin,f,'bo'); hold on;

x_ = x(1):0.1:x(end); 
y_ = (1./sqrt(8.*pi)).*exp(-((x_-mu).^2)./8); 
plot(x_,y_,'b-'); hold on;

It seems like I'm having vector size problems since it is giving me the error

Error using plot
    Vectors must be the same length.

Note that I simplified y_ since mu and the standard deviation is known.

Plot:

CodePudding user response：

Well first of all some adjustments to your question:

• You are not trying to do

  Last step: overlay the probability density function over the histogram

  The histogram being already consistent with a probability density function, it is sufficient to just overlay the density function:

  x_ = linspace(min(r),max(r),100);
  y_ = (1./sqrt(2*sigma^2*pi)).*exp(-((x_-mu).^2)./(2*sigma^2)); 
  plot(x_,y_,'b-');
  

  With N = 150

  

  With N = 1500

  

  With N = 150.000 and Nbins = 50

  

  If for some obscure reason you want to use old hist() function

  The old hist() function can't handle normalization, so you'll have to do it by hand, by normalizing your density function to fit your histogram:

  N = 1500;
  % rng('default') % For reproducibility
  mu = 5;
  sigma = 2;
  r = random('Normal',mu,sigma,1,N);
  Nbins = 50;
  [~,centers]=hist(r,Nbins);
  hist(r,Nbins); hold on
  
  % Width of bins
  Widths = diff(centers);
  
  x_ = linspace(min(r),max(r),100);
  y_ = N*mean(Widths)*(1./sqrt(2*sigma^2*pi)).*exp(-((x_-mu).^2)./(2*sigma^2)); 
  plot(x_,y_,'r-');