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# wweibfit

## PURPOSE

Parameter estimates for Weibull data.

## SYNOPSIS

[phat, cov, pci]=wweibfit(data1, plotflag);

## DESCRIPTION

``` WWEIBFIT Parameter estimates for Weibull data.

CALL:  [phat, cov] = wweibfit(data, plotflag)

phat = [a,c] = the maximum likelihood estimates of the
parameters of the Weibull distribution
(see wweibcdf) given the data.
cov  = asymptotic covariance matrix of estimates
data = data vector
plotflag = 0, do not plot
> 0, plot the empiricial distribution function and the
estimated cdf (see empdistr for options)(default)

Example:
R=wweibrnd(10,2,1,100);
[phat, cov] = wweibfit(R)

## CROSS-REFERENCE INFORMATION

This function calls:
 empdistr Computes and plots the empirical CDF wnorminv Inverse of the Normal distribution function wweibcdf Weibull cumulative distribution function deblank Remove trailing blanks. error Display message and abort function. fzero Scalar nonlinear zero finding. mean Average or mean value. optimset Create/alter OPTIM OPTIONS structure. std Standard deviation. str2num Convert string matrix to numeric array. title Graph title. version MATLAB version number.
This function is called by:
 dist2dfit Parameter estimates for DIST2D data. mdist2dfit Parameter estimates for MDIST2D data. weib2dfit Parameter estimates for 2D Weibull data. wtweibfit Parameter estimates for truncated Weibull data.

## SOURCE CODE

```001 function [phat, cov, pci]=wweibfit(data1, plotflag);
002 %WWEIBFIT Parameter estimates for Weibull data.
003 %
004 % CALL:  [phat, cov] = wweibfit(data, plotflag)
005 %
006 %     phat = [a,c] = the maximum likelihood estimates of the
007 %            parameters of the Weibull distribution
008 %            (see wweibcdf) given the data.
009 %     cov  = asymptotic covariance matrix of estimates
010 %     data = data vector
011 % plotflag = 0, do not plot
012 %          > 0, plot the empiricial distribution function and the
013 %               estimated cdf (see empdistr for options)(default)
014 %
015 % Example:
016 %   R=wweibrnd(10,2,1,100);
017 %   [phat, cov] = wweibfit(R)
018 %
020
021 % Reference: Cohen & Whittle, (1988) "Parameter Estimation in Reliability
022 % and Life Span Models", p. 25 ff, Marcel Dekker.
023
024 %Tested on: matlab  5.3
025 % History:
026 % revised pab 03.11.2000
027 % - added
028 % revised pab 24.10.2000
029 %  - added nargchk + safer call to fzero
030 %  - made sure data is a vector
031 % rewritten ms 20.06.2000
032
033 error(nargchk(1,2,nargin))
034 if nargin<2|isempty(plotflag),  plotflag=1; end
035
036 data  = data1(:);                            % make sure it is a vector
037 start = 1./(6^(1/2)/pi*std(log(data)));
038
039 mvrs=version;ix=find(mvrs=='.');
040 if str2num(mvrs(1:ix(2)-1))>5.2,
041   chat = fzero('wweibcfit',start,optimset,data);
042 else
043   chat = fzero('wweibcfit',start,sqrt(eps),[],data);
044 end
045 ahat = mean(data.^chat).^(1./chat);
046 phat = [ahat(:), chat(:)];
047
048 cov=[1.109*ahat^2/chat^2,0.257*ahat;0.257*ahat,0.608*chat^2]/length(data);
049
050 if nargout>2,
051   var=diag(cov)';
052   alpha2=ones(1,2)*0.05/2;
053   pci = wnorminv([alpha2;1-alpha2],[phat;phat],[var;var]);
054 end
055
056
057 if plotflag
058   sd=sort(data);
059   empdistr(sd,[sd, wweibcdf(sd,ahat,chat)],plotflag)
060   title([deblank(['Empirical and Weibull estimated cdf'])])
061 end
062
063```

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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