Fit all valid parametric probability distributions to data 1.0

ALLFITDIST Fit all valid parametric probability distributions to data.[D PD] = ALLFITDIST(X) fits all valid parametric probability distributions to the data in column vector X, and returns a struct D of fitted distributions and parameters and a struct of objects PD representing the fitted distributions. PD is an object in a class derived from the ProbDist class. [...] = ALLFITDIST(X,SORTBY) returns the struct of valid distributions sorted by the parameter SORTBY NLogL - Negative of the log likelihood BIC - Bayesian information criterion (default) AIC - Akaike information criterion AICc - AIC with a correction for finite sample sizes [...] = ALLFITDIST(X,SORTBY,'NAME1',VALUE1,'NAME2',VALUE2,...) follows the same input format as FITDIST, specifying optional argument name/value pairs. [...] = ALLFITDIST(...,'DISCRETE') specifies it is a discrete distribution and do not attempt to fit a continuous distribution to the data [...] = ALLFITDIST(...,'PDF') or (...,'CDF') plots either the PDF or CDF of a subset of the fitted distribution. The distributions are plotted in order of fit, according to SORTBY. List of distributions it will try to fitContinuous (default)BetaBirnbaum-SaundersExponentialExtreme valueGammaGeneralized extreme valueGeneralized ParetoInverse GaussianLogisticLog-logisticLognormalNakagamiNormalRayleighRiciant location-scaleWeibull Discrete ('DISCRETE')BinomialNegative binomialPoisson Note: If 'n' for binomial data is not given, as per FITDIST notation, then the Method of Moments estimate will be calculated. Additionally, ALLFITDIST does not handle nonparametric kernel-smoothing, use FITDIST directly instead. EXAMPLE 1Given random data from an unknown continuous distribution, find the best distribution which fits that data, and plot the PDFs to compare graphically.x = normrnd(5,3,1e4,1); %Assumed from unknown distribution[D PD] = allfitdist(x,'PDF'); %Compute and plot resultsD(1) %Show output from best fit EXAMPLE 2Given random data from a discrete unknown distribution, with frequency data, find the best discrete distribution which would fit that data, sorted by 'NLogL', and plot the CDFs to compare graphically.x = nbinrnd(20,.3,1e4,1);values=unique(x); freq=histc(x,values);[D PD] = allfitdist(values,'NLogL','frequency',freq,'CDF','DISCRETE');PD{1} EXAMPLE 3Although the Geometric Distribution is not listed, it is a special case of fitting the more general Negative Binomial Distribution. The parameter 'r' should be close to 1. Show by example.r=geornd(.7,1e4,1); %Random from Geometric[D PD]= allfitdist(r,'PDF','DISCRETE');PD{1} EXAMPLE 4Compare the resulting distributions under two different assumptions of discrete data. The first, that it is known to be derived from a Binomial Distribution with known 'n'. The second, that it may be Binomial but 'n' is unknown and should be estimated. Note the second scenario may not yield a Binomial Distribution as the best fit, if 'n' is estimated incorrectly. (Best to run example a couple times to see effect)r = binornd(10,.3,1e2,1);[D1 PD1] = allfitdist(r,'n',10,'DISCRETE','PDF'); %Force binomial[D2 PD2] = allfitdist(r,'DISCRETE','PDF'); %May be binomialPD1{1}, PD2{1} %Compare distributions

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	Compare,  Directly,  Graphically,  Random,  Results,  Unknown
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