Let [X] and {X} be the integer and the fractional parts of a random variable X. The conditional distribution function Fn(x)=P({X}≤x|[X]=n) for an integer n is investigated. Fn for a large n is regarded as the distribution of a roundoff error in an extremal event. For most well-known continuous...

In this paper we investigate asymptotic behavior of the tail probability for subordinated self-similar processes with regularly varying tail probability. We show that the tail probability of the one-dimensional distributions and the supremum tail probability are regularly varying with the...

In this paper we estimate tail probabilities for the sum of Lognormal distributions. We propose to use a defensive mixture, and develop a method of finding the optimal density via the EM algorithm; we also consider the technique which assumes the importance sampling density to belong to the same...

Let {Xi, i[greater-or-equal, slanted]1} be a sequence of i.i.d. random vectors inRd, and let[nu]p, 0p1, be a positive, integer valued random variable, independent ofXis. The[nu]-stable distributions are the weak limits of properly normalized random sums [summation...

To detect the software theft, software birthmarks have been proposed. Software birthmark systems extract software birthmarks, which are native characteristics of software, from binary programs, and compare them by computing the similarity between birthmarks. This paper proposes a new procedure...