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


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

x -> infty 
exp xp(x)
  =  1.

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