tquant.m

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function t=tquant(n, p)
%TQUANT  Quantiles of Student's t distribution
%
%  TQUANT(n, p) is the p-quantile of a t distributed random variable
%  with n degrees of freedom; that is, TQUANT(n, p) is the value below
%  which 100p percent of the t distribution with n degrees of freedom
%  lies.
  
%  Modified 13-Jul-06
%  Author: Tapio Schneider
%          [e-mail]

%  References:  
%  L. Devroye, 1986: "Non-Uniform Random Variate Generation", Springer
%  
%  M. Abramowitz and I. A. Stegun, 1964: "Handbook of Mathematical
%     Functions" 
%  
%  See also: tcdf.m in the Matlab Statistics Toolbox (evaluates
%     cumulative distribution function of Student's t)

  if (n ~= round(n) | n < 1)
    error('Usage: TQUANT(n,p) - Degrees of freedom n must be positive integer.')
  end

  if (p<0 | p>1)
    error('Usage: TQUANT(n,p) - Probability p must be in [0,1].')  
  elseif p == 1
    t   = Inf;
    return
  elseif p == 0
    t   = -Inf;
    return
  end
  
  if n == 1
    % Cauchy distribution (cf. Devroye [1986, pp. 29 and 450])
    t   = tan(pi*(p-.5));
  elseif p >= 0.5 
    % positive t-values (cf. M. Abramowitz and I. A. Stegun [1964,
    % Chapter 26])
    b0  = [0, 1];
    f   = inline('1 - betainc(b, n/2, .5)/2 - p', 'b', 'n', 'p'); 
    opt = optimset('Display', 'off'); 
    b   = fzero(f, b0, opt, n, p); 
    % old calling sequence (on Windows/Mac with older Matlab versions):
    %b   = fzero(f, b0, eps, 0, n, p); 
    
    t   = sqrt(n/b-n);
  else
    % negative t-values
    b0  = [0, 1];
    f   = inline('betainc(b, n/2, .5)/2 - p', 'b', 'n', 'p'); 
    %opt = optimset('Display', 'off'); % does not work on Windows/Mac
    %b   = fzero(f, b0, opt, n, p); 
    % old calling sequence (for Windows/Mac compatibility):
    b   = fzero(f, b0, eps, 0, n, p);  
    t   = -sqrt(n/b-n);
  end