Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / statistics-1.1.3 / gamfit.m

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+## Author: Martijn van Oosterhout <kleptog@svana.org>
+## This program is granted to the public domain.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} [A B] = gamfit (@var{R})
+## Finds the maximumlikelihood estimator for the Gamma distribution for R
+## @seealso{gampdf, gaminv, gamrnd, gamlike}
+## @end deftypefn
+
+## This function works by minimizing the value of gamlike for the vector R.
+## Just about any minimization function will work, all it has to do a
+## minimize for one variable. Although the gamma distribution has two
+## parameters, their product is the mean of the data. so a helper function
+## for the search takes one parameter, calculates the other and then returns
+## the value of gamlike.
+
+## Note: Octave uses the inverse scale parameter, which is the opposite of
+## Matlab. To work for Matlab, value of b needs to be inverted in a few
+## places (marked with **)
+
+function res = gamfit(R)
+
+  if (nargin != 1)
+    print_usage;
+  endif
+
+  avg = mean(R);
+
+  # This can be just about any search function. I choose this because it
+  # seemed to be the only one that might work in this situaition...
+  a=nmsmax( @gamfit_search, 1, [], [], avg, R );
+
+  b=a/avg;      # **
+
+  res=[a 1/b];
+endfunction
+
+# Helper function so we only have to minimize for one variable. Also to
+# inverting the output of gamlike, incase the optimisation function wants to
+# maximize rather than minimize.
+function res = gamfit_search( a, avg, R )
+  b=a/avg;      # **
+  res = -gamlike([a 1/b], R);
+endfunction