Tail asymptotics of the nth convolution of super-exponential distributions

A. Nagaev and G. Tsitsiashvili

Statistics & Probability Letters, 2006, vol. 76, issue 9, 861-870

Abstract: In this paper we consider distribution density with . Suppose that pn(x) is n-convolution of p(x) then in some regularity conditions on r(x) (in terms of h(x): slow variation, regular variation and tendency to infinity faster than any power of x) the following formula is proved: for any fixed n>1 as x-->[infinity]pn(x)=n-1/2(2[pi])(n-1)/2(r''(x/n))-(n-1)/2exp(-nr(x/n))(1+o(1)).

Keywords: Abel; theorem; Conjugate; density; Laplace's; method (search for similar items in EconPapers)
Date: 2006
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