# Histogram with superimposed fitted normal density.

function varargout = histfit2(data,nbins,dist,ploton)
%HISTFIT Histogram with superimposed fitted normal density.
%   HISTFIT(DATA,NBINS) plots a histogram of the values in the vector DATA,
%   along with a normal density function with parameters estimated from the
%   data.  NBINS is the number of bars in the histogram. With one input
%   argument, NBINS is set to the square root of the number of elements in
%   DATA.
%
%   HISTFIT(DATA,NBINS,DIST) plots a histogram with a density from the DIST
%   distribution.  DIST can take the following values:
%
%         'beta'                             Beta
%         'birnbaumsaunders'                 Birnbaum-Saunders
%         'exponential'                      Exponential
%         'extreme value' or 'ev'            Extreme value
%         'gamma'                            Gamma
%         'generalized extreme value' 'gev'  Generalized extreme value
%         'generalized pareto' or 'gp'       Generalized Pareto (threshold 0)
%         'inverse gaussian'                 Inverse Gaussian
%         'logistic'                         Logistic
%         'loglogistic'                      Log logistic
%         'lognormal'                        Lognormal
%         'negative binomial' or 'nbin'      Negative binomial
%         'nakagami'                         Nakagami
%         'normal'                           Normal
%         'poisson'                          Poisson
%         'rayleigh'                         Rayleigh
%         'rician'                           Rician
%         'tlocationscale'                   t location-scale
%         'weibull' or 'wbl'                 Weibull
%
%   H = HISTFIT(...) returns a vector of handles to the plotted lines.
%   H(1) is a handle to the histogram, H(2) is a handle to the density curve.

%   Copyright 1993-2008 The MathWorks, Inc.
%   $Revision: 1.1.8.3$  $Date: 2010/12/22 16:31:43$

if ~isvector(data)
error(message('stats:histfit:VectorRequired'));
end

data = data(:);
data(isnan(data)) = [];
n = numel(data);

if nargin<2 || isempty(nbins)
nbins = ceil(sqrt(n));
elseif ~isscalar(nbins) || ~isnumeric(nbins) || ~isfinite(nbins) ...
|| nbins~=round(nbins)
end

% Do histogram calculations
[bincounts,bincenters]=hist(data,nbins);

% Fit distribution to data
if nargin<3 || isempty(dist)
dist = 'normal';
end
try
pd = fitdist(data,dist);
catch myException
if isequal(myException.identifier,'stats:ProbDistUnivParam:fit:NRequired')
% Binomial is not allowed because we have no N parameter
else
% Pass along another other errors
throw(myException)
end
end

% Find range for plotting
q = icdf(pd,[0.0013499 0.99865]); % three-sigma range for normal distribution
x = linspace(q(1),q(2)*2);
if ~pd.Support.iscontinuous
% For discrete distribution use only integers
x = round(x);
x(diff(x)==0) = [];
end

% Compute the normalized histogram
binwidth = median(diff(bincenters)); % Finds the width of each bin.
area = numel(data(:)) * binwidth; % total area to normalize the pdf
xd = bincenters;
yd = bincounts./area;

% Plot the histogram with no gap between bars.
if ploton
hh = bar(xd,yd,[min(data), max(data)],'hist');
set(hh,'EdgeColor','none','FaceColor','g')

% Probability density function of the histogram
y = pdf(pd,x);

% Overlay the density
np = get(gca,'NextPlot');
if ploton
hh1 = plot(x,y,'k-','LineWidth',3);
end

if nargout == 1
h = [hh; hh1];
end

set(gca,'NextPlot',np)

h = [hh; hh1];
else
h = 0;
end

argout={h,pd,[xd',yd']};

if nargout > length(argout)
error('Too many output arguments.');
end

[varargout{1:nargout}]=argout{1:nargout};

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