Simulation results for the asymptotic scaled capture-zone distribution (CZD) for the case of irreversible nucleation and growth of point islands are presented for substrate dimension d=1 , 2, 3, and 4 and compared with a recent conjecture based on the Wigner distribution. Poor agreement is found between the predicted Wigner distributions and the asymptotic CZD in the limit of infinite DF (corre...

Logarithmic general error distribution, an extension of the log-normal distribution, is proposed. Some interesting properties of the logarithmic general error distribution are derived. These properties are applied to establish the asymptotic behavior of the ratio of probability densities and the ratio of the tails of the logarithmic general error and log-normal distributions, and to derive the ...

We investigate multiple Charlier polynomials and in particular we will use the (nearest neighbor) recurrence relation to find the asymptotic behavior of the ratio of two multiple Charlier polynomials. This result is then used to obtain the asymptotic distribution of the zeros, which is uniform on an interval. We also deal with the case where one of the parameters of the various Poisson distribu...

In this paper, we prove a result for the asymptotic distribution of the sample average value-at-risk (AVaR) under certain regularity assumptions. The asymptotic distribution can be used to derive asymptotic confidence intervals when AV aR2(X) is calculated by the Monte Carlo method which is adopted in many risk management systems. We study the effect of the tail behavior of the random variable ...

Two types of M-estimators of the parameters of the multi-variate linear model are considered. The first type corresponds to coordinatewise M-estimators; the second is an extension of Maronna's (1976) proposal for the multivariate location case. Under some general conditions on the error distribution, on the design matrix and on the score functions, the asymptotic distribution of the coordinatew...

We consider the classical M/G/1 queue with two priority classes and the nonpreemptive and preemptive-resume disciplines. We show that the low-priority steady-state waiting-time can be expressed as a geometric random sum of i.i.d. random variables, just like the M/G/1 FIFO waiting-time distribution. We exploit this structures to determine the asymptotic behavior of the tail probabilities. Unlike...

We consider two-player random extensive form games where the payoffs at the leaves are independently drawn uniformly at random from a given feasible set C. We study the asymptotic distribution of the subgame perfect equilibrium outcome for binarytrees with increasing depth in various random (or deterministic) assignments of players to nodes. We characterize the assignments under which the asymp...

We study numerically a non-linear integral equation that arises in the study of binary search trees. If the tree is constructed from n elements, this integral equation describes the asymptotic (as n → ∞) distribution of the height of the tree. The height is defined as the longest path in the tree. Our analysis supplements some asymptotic results we recently obtained (cf. Knessl and Szpankowski ...