We show that the weak Pareto law, as used to characterize the tail behaviour of income distributions, implies regularly varying tail probabilities, but that the reverse implication does not hold. We also establish implications among other versions of the weak Pareto law.

Recent advances in social science surveys include collection of biological samples. Although biomarkers offer a large potential for social science and economic research, they impose a number of statistical challenges, often being distributed asymmetrically with heavy tails. Using data from the...

This paper seeks to identify computationally efficient importance sampling (IS) algorithms for estimating large deviation probabilities for the loss on a portfolio of loans. Related literature typically assumes that realised losses on defaulted loans can be predicted with certainty, i.e., that...

A certain spectrum, indexed by a\in[0,\infty], of upper bounds P_a(X;x) on the tail probability P(X\geq x), with P_0(X;x)=P(X\geq x) and P_\infty(X;x) being the best possible exponential upper bound on P(X\geq x), is shown to be stable and monotonic in a, x, and X, where x is a real number and X...

We show that the weak Pareto law, as used to characterize the tail behaviour of income distributions, implies regularly varying tail probabilities, but that the reverse implication does not hold. We also establish implications among other versions of the weak Pareto law.

Asymptotic expansions for large deviation probabilities are used to approximate the cumulative distribution functions of noncentral generalized chi-square distributions, preferably in the far tails. The basic idea of how to deal with the tail probabilities consists in first rewriting these...

We consider the problem of precise estimation of service-level measures in multistage production-inventory systems when the system is managed for high levels of service. Precisely because the service level is high, stockouts, large backorders, and unfilled demands are rare and thus difficult to...

We show that the weak Pareto law, as used to characterize the tail behaviour of income distributions, implies regularly varying tail probabilities, but that the reverse implication does not hold. We also establish implications among other versions of the weak Pareto law.

In this article we consider the efficient estimation of the tail distribution of the maximum of correlated normal random variables. We show that the currently recommended Monte Carlo estimator has difficulties in quantifying its precision, because its sample variance estimator is an inefficient...

Recent advances in social science surveys include collection of biological samples. Although biomarkers offer a large potential for social science and economic research, they impose a number of statistical challenges, often being distributed asymmetrically with heavy tails. Using data from the...