[S] In search of a density

andrey@utstat.toronto.edu
Mon, 26 Oct 98 10:48 EST


Wolfgang Rolke asked:
I have a rather strange question: I am looking for a symmetric unimodal
density with support on the whole real line with tails that die off not
slower than a standard normal and an explicit expression for the inverse
of the cumulative distribution function. Something like the double
exponential would do, only its tails are to heavy...

This one, although elementary, was tricky; hope it's not too inappropriate
to post a solution here: One such density is:

f(x) = C if |x| < 1 and
f(x) = C*(x^2)*exp(-abs(x^3)) if |x| > 1.

where C = 3e/(6e+2). (Yes, it was a rather strange question!)

Andrey Feuerverger, Toronto.
andrey@utstat.toronto.edu

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