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) See also wtraylcdf, wraylfit
Computes and plots the empirical CDF | |
Log-likelihood function. | |
Inverse of the Normal distribution function | |
Truncated Rayleigh cumulative distribution function | |
Remove trailing blanks. | |
Display message and abort function. | |
Multidimensional unconstrained nonlinear minimization (Nelder-Mead). | |
Create/alter OPTIM OPTIONS structure. | |
Convert string matrix to numeric array. | |
Graph title. | |
MATLAB version number. |
Parameter estimates for DIST2D data. |
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 % 019 % See also wtraylcdf, wraylfit 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 034 % - added nargchk 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
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