function [chi2]=wilhil(nu,p) 
% Syntax: [chi2]=wilhil(nu,p); 
% Wilson-Hilferty approximation to chi-squared. 
%  
% Inputs: p - single-tailed probability 
%         nu - degrees of freedom. 
% 
% The accuracy of the approximation is relatively 
% poor for very small p and nu. The approximation 
% is systematically low for small p and nu, and 
% systematically large for large p and nu. 
%  
% Accuracy will be within 1% for the following: 
%     p = 0.005,  nu > 13.  
%     p = 0.01,   nu > 12.  
%     p = 0.025,  nu > 8.  
%     p = 0.05,   nu > 5. 
%     p = 0.95,   nu > 1. 
% 
% More accurate results  (at the cost of speed) 
% may be obtained using P. R. Shaw's 'chitable.m', 
% available on the Mathworks ftp site. 
% 
% Either p or nu may be a vector, in which case  
% the output will be a matrix.  
% For example, wilhil(1:7, [.005 .05 .95 .995]) 
% will produce a table with 4 columns and 7 rows, 
% containing the appropriate values of chi-squared. 
% 
% See e. g. Kendall and Stuart, Adv. Theory of  
% Statistics, Vol. 1, 1969. 
% 
% Written by Eric Breitenberger, version 10/8/95 
% Please send comments and suggestions to eric@gi.alaska.edu 
 
z=sqrt(2)*erfinv(2*p-1); % single-tailed 
sig=2./(9*nu); 
mu=1-sig; 
sig=sqrt(sig); 
if length(z)>1,  
  chi2=zeros(length(nu),length(z)); 
  for i=1:length(z) 
    t1=nu.*(sig.*z(i)+mu).^3; 
    chi2(:,i)=t1'; 
  end 
else   
  chi2=nu.*(sig*z+mu).^3; 
end