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For a given value of the location parameter say it is 0. Why does the median equal the location parameter. I'm slightly confused by what the location parameter actually represents? Any help would be much appreciated.

Sal1
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    In the case of the Cauchy, the point about which that density function is symmetrical. Then since total area under the density curve is $1$, the location parameter turns out to be the median. – André Nicolas Mar 08 '15 at 15:17
  • Also you know for the cauchy distribution why is it the case that when calculating the fisher information this is independent of the location parameter. – Sal1 Mar 08 '15 at 15:20

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