Verify distribution uniformity/Chi-squared test: Difference between revisions

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@@ Line 742: / Line 742: @@
 enough for the χ2 distribution to be used.
-The implementation of `Chi2_cdf` below is intended to be fairly
+The implementation of `Chi2_cdf` here uses the recursion relation for
-simple and robust rather than highly accurate.  For an
+the gamma function and should be both fast, accurate and quite robust.
-industrial-strength algorithm, see
+For an industrial-strength algorithm, see
 e.g. https://people.sc.fsu.edu/~jburkardt/c_src/asa239/asa239.c
@@ Line 760: / Line 760: @@
 # Cumulative density function of the chi-squared distribution with $k
 # degrees of freedom
+# The recursion formula for gamma is used for efficiency and robustness.
-# Use lgamma to avoid $x^m (for large $x and large m) and
-# to avoid calling gamma for large $k
 def Chi2_cdf($x; $k):
   if $x == 0 then 0
   elif $x > (1e3 * $k) then 1
   else 1e-15 as $tol  # for example
-  | { s: 0, m: 0, term: $tol}
+  | { s: 0, m: 0, term: (1 / ((($k/2)+1)|gamma)) }
   | until (.term|length < $tol; # length here is abs
+      .s += .term
-      # .term = (pow($x/2; .m) / (($k/2 + .m + 1)|gamma))
+      | .m += 1
-        .term = (((.m * (($x/2)|log)) - (($k/2 + .m + 1)|lgamma)) | exp)
-      | .s += .term
+      | .term *= (($x/2) / (($k/2) + .m )) )
+  | .s * ( ((-$x/2) + ($k/2)*(($x/2)|log)) | exp)
-      | .m += 1)
-  | .s * ( (-$x/2) + ($k/2)*(($x/2)|log)|exp)
   end ;
 </syntaxhighlight>
@@ Line 824: / Line 822: @@
 task
 </syntaxhighlight>
-{{output}}
 <pre>
 Dataset: [199809,200665,199607,200270,199649]