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# wtraylfit

## PURPOSE

Parameter estimates for Truncated Rayleigh data.

## SYNOPSIS

[phat,cov,pci] = wtraylfit(data,plotflag)

## DESCRIPTION

``` WTRAYLFIT Parameter estimates for Truncated Rayleigh data.

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

phat  = maximum likelihood estimate of the parameter of
the distribution (see wtraylcdf)
cov   = estimated asymptotic covariance of phat
data  = data matrix
plotflag = 0, do not plot
> 0, plot the empiricial distribution function and the
estimated cdf (see empdistr for options)(default)

Example:
R=wraylrnd(2,200,1);
R=R(R>1)-1;   % Truncated Raylay with b=2, c=-1
[phat cov]=wtraylfit(R)

## CROSS-REFERENCE INFORMATION

This function calls:
 empdistr Computes and plots the empirical CDF loglike Log-likelihood function. wnorminv Inverse of the Normal distribution function wtraylcdf Truncated Rayleigh cumulative distribution function deblank Remove trailing blanks. error Display message and abort function. fmins fminsearch Multidimensional unconstrained nonlinear minimization (Nelder-Mead). optimset Create/alter OPTIM OPTIONS structure. 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.

## SOURCE CODE

```001 function [phat,cov,pci] = wtraylfit(data,plotflag)
002 %WTRAYLFIT Parameter estimates for Truncated Rayleigh data.
003 %
004 % CALL:  [phat cov] = wtraylfit(data, plotflag)
005 %
006 %   phat  = maximum likelihood estimate of the parameter of
007 %           the distribution (see wtraylcdf)
008 %   cov   = estimated asymptotic covariance of phat
009 %   data  = data matrix
010 %plotflag = 0, do not plot
011 %         > 0, plot the empiricial distribution function and the
012 %              estimated cdf (see empdistr for options)(default)
013 %
014 % Example:
015 %   R=wraylrnd(2,200,1);
016 %   R=R(R>1)-1;   % Truncated Raylay with b=2, c=-1
017 %   [phat cov]=wtraylfit(R)
018 %
020
021 % Reference: Cohen & Whittle, (1988) "Parameter Estimation in Reliability
022 % and Life Span Models", p. 181 ff, Marcel Dekker.
023
024 %tested on: matlab 5.x
025 % History:
026 %  by Per A. Brodtkorb 17.10.98
027 % revised ms 15.06.2000
028 % - updated header info
029 % - changed name to wraylfit (from raylfit)
030 % revised ms 11.08.2000
031 % - changed to standard *fit form
032 % -revised pab 24.10.2000
033 %  - replaced gamma with gammaln -> more robust
035 % revised PJ 03-Apr-2001
036 %  - fmins changed name to fminsearch for version >= 5.3
037 % Revised pab Dec2003
038
039 error(nargchk(1,2,nargin))
040 if nargin<2|isempty(plotflag),  plotflag=1; end
041 data = data(:);
042 n = length(data);
043 phat = sqrt(sum(data.^2)/n/2); % Initial guess (MLE with c=0)
044
045 mvrs=version;ix=find(mvrs=='.');
046 if str2num(mvrs(1:ix(2)-1))>5.2,
047   phat = fminsearch('loglike', [phat 0],optimset,data,'wtraylpdf');
048 else
049   phat = fmins('loglike', [phat 0],[],[],data,'wtraylpdf');
050 end
051
052 if nargout > 1
053    [L, cov] = loglike(phat,data,'wtraylpdf');
054 end
055
056
057 if nargout>2,
058   var=diag(cov)';
059   alpha2=ones(1,2)*0.05/2;
060   pci = wnorminv([alpha2;1-alpha2],[phat;phat],[var;var]);
061 end
062
063 if plotflag
064   sd = sort(data);
065   empdistr(sd,[sd,wtraylcdf(sd,phat(1),phat(2))],plotflag )
066   title([deblank(['Empirical and truncated Rayleigh estimated cdf'])])
067 end
068
069
070
071```

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

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