Daniel@0: function P = chisquared_prob(X2,v)
Daniel@0: %CHISQUARED_PROB computes the chi-squared probability function.
Daniel@0: %   P = CHISQUARED_PROB( X2, v ) returns P(X2|v), the probability
Daniel@0: %   of observing a chi-squared value <= X2 with v degrees of freedom.
Daniel@0: %   This is the probability that the sum of squares of v unit-variance
Daniel@0: %   normally-distributed random variables is <= X2.
Daniel@0: %   X2 and v may be matrices of the same size size, or either 
Daniel@0: %   may be a scalar.
Daniel@0: %   
Daniel@0: %   e.g., CHISQUARED_PROB(5.99,2) returns 0.9500, verifying the
Daniel@0: %   95% confidence bound for 2 degrees of freedom. This is also
Daniel@0: %   cross-checked in, e.g., Abramowitz & Stegun Table 26.8
Daniel@0: %
Daniel@0: %   See also CHISQUARED_TABLE
Daniel@0: %
Daniel@0: %Peter R. Shaw, WHOI
Daniel@0: 
Daniel@0: % References: Press et al., Numerical Recipes, Cambridge, 1986;
Daniel@0: % Abramowitz & Stegun, Handbook of Mathematical Functions, Dover, 1972.
Daniel@0: 
Daniel@0: % Peter R. Shaw, Woods Hole Oceanographic Institution
Daniel@0: % Woods Hole, MA 02543
Daniel@0: % (508) 457-2000 ext. 2473  pshaw@whoi.edu
Daniel@0: % March, 1990; fixed Oct 1992 for version 4
Daniel@0: 
Daniel@0: % Computed using the Incomplete Gamma function,
Daniel@0: % as given by Press et al. (Recipes) eq. (6.2.17)
Daniel@0: 
Daniel@0: % Following nonsense is necessary from Matlab version 3 -> version 4
Daniel@0: versn_str=version; eval(['versn=' versn_str(1) ';']);
Daniel@0: if versn<=3, %sigh
Daniel@0:  P = gamma(v/2, X2/2);
Daniel@0: else
Daniel@0:  P = gammainc(X2/2, v/2);
Daniel@0: end