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XMM-Newton Science Analysis System


ssclib (ssclib-3.33.4) [xmmsas_20080701_1801-8.0.0]

Meta Index / Home Page / Poissonian statistics and source

`Degrees of freedom' for a sum of likelihoods

  function calcChi2HalfDegFree(numLikelihoods) result(f)
    integer(int16), intent(in) :: numLikelihoods
    real(single)               :: f
  end function calcChi2HalfDegFree

A sum over likelihoods seems to have a probability distribution similar to that of a $\chi ^2$ distribution with $2f$ degrees of freedom. The factor $f$ is approximately equal to the number of likelihoods in the sum but not quite. However for the time being (until more accurate information is available, that is) it is assumed that the equality holds exactly.