Centre for Discrete and Applicable Mathematics

CDAM Research Report, LSE-CDAM-98-02

February 1998

A shift measure for the thickness of tails

A.J. Ostaszewski

Abstract

By analogy with the hazard-rate, we propose to measure tail thickness of a cumulative distribution function F(x) by means of a shift function p(x) >= 0 defined by

f(x) = F(-x+p(x)),

where f(x) = F'(x) is the density function. We show that in the case of the standard normal distribution p(x) is asymptotic to (ln x)/x, i.e. that

lim
x -> infty

exp xp(x)

= 1.

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		CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K.
		Phone: +44(0)-171-955 7732. Fax: +44(0)-171-955 6877. Email: info@maths.lse.ac.uk