t_alpha.m

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function [alpha]=t_alpha(t, nu)
% % t_alpha:  cumulative probability function of the t-distribution, 
% %
% % Syntax='';
% %
% % [alpha]=t_alpha(t, nu);
% %
% % ***********************************************************
% %
% % Description
% %
% % This program calculates the student-t confidence level given
% % the statistic t, with nu degrees of freedom.  t can be a vector.  
% % t can handle values of -Inf, 0, and Inf. nu should be a constant.  
% %
% % In more technical language this program is the cumulative probability 
% % density function for the t-distribution.  
% %
% % For t less than 0, the alpha is less than 0.5.
% %
% % t=1 is the default measured value of the statistic.
% %
% % nu is the number of degrees of freedom.  The default value of nu is Inf.
% %    By default the normal distribution approximation is used.
% %
% % For values of nu in the range 1 <= nu <= 170,  analytical solutions
% % are used and the accuracy can be to machine precision.
% %
% % For values of nu in the range 171 <= nu <= 320, the generalized
% % hypergeometric funciton solution is used.  Some of the numbers are quite
% % large and rounding errors and other computation problems are a
% % possiblility.  The tolerance is hard coded to 10.^(-15).  Calculations
% % can have 8 digits or more of accuracy; however,
% % compuational problems can arise.
% %
% % For values of nu in the range 321 <= nu <= Inf, the normal distribution
% % approximation is used, because the hypergeometric function crashes due
% % to computational problems (large numers and small step sizes).
% %
% % ***********************************************************
% %
% % Input Variables
% %
% % t is the measured statistic value -Inf < t < Inf.
% %
% % nu is the number of degree of freedom 1 <= nu < Inf.
% %
% % ***********************************************************
% %
% % Output Variables
% %
% % alpha   % student-t level of significance, cumulative probability
% %
% % ***********************************************************
% %
% Example='';
%
% t=1;         % statistic
% nu=Inf;      % number of degrees of freedom
%
% [alpha]=t_alpha(t, nu);
%
% t=1;
% nu=10;
% [alpha2]=t_alpha(t, nu);
%
% %
% % ***********************************************************
% %
% % This program was written by Edward L. Zechmann
% %
% %     date 20 January   2008
% %
% % modified 30 January   2008   made regimes integrate from t0=0.