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📄 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%          tapio@gps.caltech.edu%  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

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