We study the estimation of conditional tail moment, defined for a non-negative random variable X as θβ,p=E(Xβ|X>U(1/p)), β>0, p∈(0,1), provided E(Xβ)<∞, where U denotes quantile function given by U(x)=inf⁡{y:F(y)⩾1−1/x}, x>1, associated to distribution F X. The focus will be on situations p is small, i.e., smaller than 1/n, n number observations that available estimation. This situation corresp...

Consider the problem of approximating the tail probability of randomly weighted sums ∑n i=1 ΘiXi and their maxima, where {Xi, i ≥ 1} is a sequence of identically distributed but not necessarily independent random variables from the extended regular variation class and {Θi, i ≥ 1} is a sequence of nonnegative random variables, independent of {Xi, i ≥ 1} and satisfying certain moment conditions. ...

We consider the first passage percolation model on the Zd lattice. In this model, we assign independently to each edge e a non-negative passage time t(e) with a common distribution F . Let a0,n be the passage time from the origin to (n, 0, · · · , 0). Under the exponential tail assumption, Kesten (1993) and Talagrand (1995) investigated the concentration of a0,n from its mean using different me...

We consider the cyclic polling system with two queues. One queue is served according to the exhaustive discipline, and the other queue is served according to the 1-limited discipline. At least one of the service and/or switchover times has a regularly varying tail. We obtain the tail behavior of the waiting time distributions. When one of the service and/or switchover times has an infinite seco...

A great diversity of unicellular and invertebrate organisms swim along a helical path, but it is not well understood how asymmetries in the body shape or the movement of propulsive structures affect a swimmer's ability to perform the body rotation necessary to move helically. The present study found no significant asymmetries in the body shape of ascidian larvae (Distaplia occidentalis) that co...

This note proposes a new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables. The unknown parameters are determined by the first four cumulants of the quadratic forms. The proposed method is compared with Pearson’s three-moment central χ2 approximation approach, by means of numerical examples. Our method yields a better approxima...

The moment’s estimator (Dekkers et al., 1989) has been used in extreme value theory to estimate the tail index, but it is not location invariant. The location invariant Hill-type estimator (Fraga Alves, 2001) is only suitable to estimate positive indices. In this paper, a new moment-type estimator is studied, which is location invariant. This new estimator is based on the original moment-type e...

Suppression of head-tail effects on turn-by-turn BPM measurements V. Lebedev The study carried out for BLT proved that the head-tail motion excited by the machine chromaticity could seriously affect the performance of turn-by-turn BPM measurements. In this paper I consider how this problem can be alleviated for new Tevatron BPMs. Let us consider the case when the bunch, which initially was on t...