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  1. Commons Math
  2. MATH-1257

NormalDistribution.cumulativeProbability() suffers from cancellation

    Details

    • Type: Bug
    • Status: Closed
    • Priority: Minor
    • Resolution: Fixed
    • Affects Version/s: 3.5
    • Fix Version/s: 4.0, 3.6
    • Labels:
      None

      Description

      I see the following around line 194:

              return 0.5 * (1 + Erf.erf(dev / (standardDeviation * SQRT2)));
      

      When erf() returns a very small value, this cancels in the addition with the "1.0" which leads to poor precision in the results.

      I would suggest changing this line to read more like:

      return 0.5 * Erf.erfc( -dev / standardDeviation * SQRT2 );
      

      Should you want some test cases for "extreme values" (one might argue that within 10 standard deviations isn't all that extreme) then you can check the following: http://www.jstatsoft.org/v52/i07/ then look in the v52i07-xls.zip at replication-01-distribution-standard-normal.xls

      I think you will also find that evaluation of expressions such as

      NormalDistribution( 0, 1 ).cumulativeProbability( -10.0 );

      are pretty far off.

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            • Assignee:
              Unassigned
              Reporter:
              murphyw Bill Murphy
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