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histfit.m

## Copyright (C) 2003 Alberto Terruzzi
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; If not, see <http://www.gnu.org/licenses/>.

## usage:  histfit(data,nbins)
##
## Histogram with superimposed fitted normal density.
##
## histfit(data,nbins) plots a histogram of the values in the vector data.
## using nbins bars in the histogram. With one input argument, nbins is set 
## to the square root of the number of elements in data. 
##
## Example
##
##   histfit(randn(100,1))
##
## See also bar,hist and pareto.

## Author: Alberto Terruzzi <t-albert@libero.it>
## Version: 1.0
## Created: 3 March 2004

function histfit (data,nbins)

if nargin < 1 || nargin > 2
  usage("histfit (data,nbins)")
endif

if isvector (data) != 1
  error ("data must be a vector.");
endif

row = sum(~isnan(data));

if nargin < 2
  nbins = ceil(sqrt(row));
endif

[n,xbin]=hist(data,nbins);
if any(abs(diff(xbin,2)) > 10*max(abs(xbin))*eps)
  error("histfit bins must be uniform width");
endif

mr = nanmean(data); ## Estimates the parameter, MU, of the normal distribution.
sr = nanstd(data);  ## Estimates the parameter, SIGMA, of the normal distribution.
x=(-3*sr+mr:0.1*sr:3*sr+mr)';## Evenly spaced samples of the expected data range.
[xb,yb] = bar(xbin,n);
y = normal_pdf(x,mr,sr.^2);  
binwidth = xbin(2)-xbin(1);
y = row*y*binwidth;   ## Normalization necessary to overplot the histogram.
plot(xb,yb,";;b",x,y,";;r-");     ## Plots density line over histogram.

endfunction


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