Page "Cauchy distribution" Paragraph 53

Higher even-powered raw moments will also evaluate to infinity.

Odd-powered raw moments, however, do not exist at all ( i. e. are undefined ), which is distinctly different from existing with the value of infinity.

( Consider 1 / 0, which is defined with the value of infinity, vs. 0 / 0, which is undefined.

) The odd-powered raw moments are undefined because their values are essentially equivalent to since the two halves of the integral both diverge and have opposite signs.

The first raw moment is the mean, which, being odd, does not exist.

( See also the discussion above about this.

) This in turn means that all of the central moments and standardized moments do not exist ( are undefined ), since they are all based on the mean.

The variance — which is the second central moment — is likewise non-existent ( despite the fact that the raw second moment exists with the value infinity ).