DistributionFit

Fits normal, lognormal, and weibull distributions to data

%function [pdffit,offset,A,B,resnorm,mode,medpdf,ndata,h] = distributionfit(data,distribution,nbins,figureWH)
%PURPOSE jdc rev. 23-Mar-06
% Fit one of three probability distributions (normal, lognormal, weibull)
% to input data vector. If the distribution is specified as 'best' the dis-
% tribution that best fits the data is selected automatically.
%INPUT
% If nargin==1, "distribution" is prompted for and entered interactively
%
% data - n x 1 or 1 x n input data vector
% distribution - probability distribution to fit to "data". Can
% be 'normal', 'lognormal', 'weibull', or 'best' ... default: 'best'
% nbins - number of bar-chart bins ................................... default: sqrt(length(data))
% figureWH - figure size [width height] (inches) ????... default: [4 3]
%OUTPUT
% pdffit - fitted probability density function - n x 2 matrix with column 1 the
% x-values, column 2 the y values
% offset - amount by which the data was offset for lognormal and weibull fits
% (to satisfy the positive-definite requirements for these distributions).
% Note: this is approximately equivalent to fitting a 3- rather than a 2-parameter
% distribution.
% A,B - distribution parameters - mu and sigma for normal and lognormal distributions,
% scale and shape parameters for weibull distribution
% resnorm - measure of goodness of fit: sum of squares of point-by-point differences
% between experimental and best-fit cumulative distribution function
% mode - 2-element vector: [distribution mode density at mode]
% medpdf - 2-element vector: [data median pdf density at median]
% h - handles to the bar chart and probability density curve
%
%TYPICAL FUNCTION CALLS (using random number vectors for input data)
% distributionfit(randn(10000,1));
% distributionfit(wblrnd(2,3,10000,1));
% distributionfit(wblrnd(2,3,10000,1),'weibull');
% distributionfit(lognrnd(1.5,.5,10000,1),'lognormal');
% distributionfit(lognrnd(1.5,.5,10000,1),'best');
%REFERENCE
% Statistics Toolbox Version 3.0.2, function HISTFIT.M
%REVISIONS
% 09jun05 Revised pdf plot to reflect input rather than zero-shifted data
% " Fixed some problems with lognormal distribution related to
% logarithms and exponents of very small numbers
% 10jun05 Added mode and median to arguments out
% 23mar06 Set xlim(2) to max(data)
% " Decreased text fontsize & fixed text placement problem