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# braylfit

## PURPOSE

Parameter estimates for Beta-Rayleigh data.

## SYNOPSIS

[phat, cov,pci]=braylfit(data1,alpha)

## DESCRIPTION

``` BRAYLFIT Parameter estimates for Beta-Rayleigh data.

CALL: [phat,cov, pci] = braylfit(data,alpha);

phat  = [a, b, c] = maximum likelihood estimates of the
parameters of the Beta-Rayleigh distribution (see
braylpdf) given the data.
cov   = asymptotic covariance matrix of estimates
pci   = 100*(1-alpha) percent confidense intervals
data  = data matrix
alpha = confidence level (default 0.05 corresponding to 95% CI)

Example:
a = .9; b = 105; sz = [100,1]
R = sort(wbetarnd(a,b,sz));
phat = braylfit(R)
empdistr(R,[R braylpdf(R,p(1),p(2),p(3))])

## CROSS-REFERENCE INFORMATION

This function calls:
 loglike Log-likelihood function. wbetafit Parameter estimates for Beta data. wnorminv Inverse of the Normal distribution function error Display message and abort function. fmins fminsearch Multidimensional unconstrained nonlinear minimization (Nelder-Mead). str2num Convert string matrix to numeric array. version MATLAB version number.
This function is called by:

## SOURCE CODE

```001 function [phat, cov,pci]=braylfit(data1,alpha)
002 %BRAYLFIT Parameter estimates for Beta-Rayleigh data.
003 %
004 % CALL: [phat,cov, pci] = braylfit(data,alpha);
005 %
006 %   phat  = [a, b, c] = maximum likelihood estimates of the
007 %           parameters of the Beta-Rayleigh distribution (see
008 %           braylpdf) given the data.
009 %   cov   = asymptotic covariance matrix of estimates
010 %   pci   = 100*(1-alpha) percent confidense intervals
011 %   data  = data matrix
012 %   alpha = confidence level (default 0.05 corresponding to 95% CI)
013 %
014 % Example:
015 %  a = .9; b = 105; sz = [100,1]
016 %  R = sort(wbetarnd(a,b,sz));
017 %  phat = braylfit(R)
018 %  empdistr(R,[R braylpdf(R,p(1),p(2),p(3))])
019 %
021
022 % tested on: matlab 5.2
023 %History:
024
025 % revised pabnov 2004
026 % -replaced fmins with fminsearch
027 % by Per A. Brodtkorb 14.02.99
028 %   Reference:
029
030 error(nargchk(1,2,nargin))
031 if (nargin < 2)|isempty(alpha)
032     alpha = 0.05;
033 end
034 p_int = [alpha/2; 1-alpha/2];
035
036 data1=data1(:)
037
038 c=sqrt(2)*max(data1);
039 pinit=[wbetafit((data1./c).^2) c]
040
041 %simultanous MLE
042 mvrs=version;ix=find(mvrs=='.');
043 if str2num(mvrs(1:ix(2)-1))>5.2,
044   phat = fminsearch('loglike',pinit,[],data1,'braylpdf');
045 else
046   phat = fmins('loglike',pinit,[],[],data1,'braylpdf');
047 end
048
049 % Old call
050 %phat = fmins('brayllike',pinit,[],[],data1);
051
052
053 if nargout >1
054    [L, cov] = loglike(phat,data1,'braylpdf')
055    %[logL,cov]=brayllike(phat,data1); % old call
056    sigma = diag(cov).';
057    pci = wnorminv(repmat(p_int,1,2),[phat; phat],[sigma;sigma]);
058  end
059
060
061```

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

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