Show that the median of a univariate density that can be approximated by an Edgeworth series occurs approximately at the point xˆ =

−κ3 6κ2

.

Hence show that, to the same order of approximation, in the univariate case,

(mean−median)

(mean−mode) =

1 3

(Haldane, 1942). See also Haldane (1948) for a discussion of medians of multivariate distributions.