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## Asymptotics and Uniform Bounds for Multiclass Queueing Networks

### Stochastic Networks (1996-01-01) 117: 65-73 , January 01, 1996

Recently it has been shown in [2] that one can obtain linear programs which provide bounds on the coefficients *α, v* in the expression
$$ \frac{{\alpha N}}{{N + \nu }} $$
, which then bound the throughput for every population size *N* in a closed irreducible network. Also, it has been shown in [1] that one can obtain linear programs which provide bounds on the coefficients {*c*_{i}} in the expansion
$$ \sum\nolimits_{{i = 0}}^{M} {\tfrac{{{{c}_{i}}\rho }}{{{{{(1 - \rho )}}^{i}}}}} $$
, which then bounds the mean number in an open system for every nominal load *p* in the system. We provide a brief account of these results.

## Bayesian calibration in the estimation of the age of rhinoceros

### Annals of the Institute of Statistical Mathematics (1996-03-01) 48: 17-28 , March 01, 1996

In this paper the Bayesian approach for nonlinear multivariate calibration will be illustrated. This goal will be achieved by applying the Gibbs sampler to the rhinoceros data given by Clarke (1992, *Biometrics*, *48*(4), 1081–1094). It will be shown that the point estimates obtained from the profile likelihoods and those calculated from the marginal posterior densities using improper priors will in most cases be similar.

## Kaplan-Meier Survival Curves and the Log-Rank Test

### Survival Analysis (1996-01-01): 45-82 , January 01, 1996

We begin with a brief review of the purposes of survival analysis, basic notation and terminology, and the basic data layout for the computer.

## An identity for the product moments of order statistics

### Metrika (1996-12-01) 44: 95-100 , December 01, 1996

A general identity for the product moments of successive order statistics is given, which is valid in a class of probability distributions including Weibull, Pareto, exponential and Burr distributions.

## Derivation of the probability distribution functions for succession quota random variables

### Annals of the Institute of Statistical Mathematics (1996-09-01) 48: 551-561 , September 01, 1996

The probability distribution functions (pdf's) of the sooner and later waiting time random variables (rv's) for the succession quota problem (*k* successes and *r* failures) are derived presently in the case of a binary sequence of order *k*. The probability generating functions (pgf's) of the above rv's are then obtained directly from their pdf's. In the case of independent Bernoulli trials, expressions for the pdf's in terms of binomial coefficients are also established.

## Hierarchy as a Clustering Structure

### Mathematical Classification and Clustering (1996-01-01) 11: 329-397 , January 01, 1996

Directions for representing and comparing hierarchies are discussed.

Clustering methods that are invariant under monotone dissimilarity transformations are analyzed.

Most recent theories and methods concerning such concepts as ultrametric, tree metric, Robinson matrix, pyramid, and weak hierarchy are presented.

A linear theory for binary hierarchy is proposed to allow decomposing the data entries, as well as covariances, by the clusters.

## Back Matter - Environmental Studies

### Environmental Studies (1996-01-01): 79 , January 01, 1996

## Control Representation in an EDA Assistant

### Learning from Data (1996-01-01) 112: 353-362 , January 01, 1996

To develop an initial understanding of complex data, one often begins with exploration. Exploratory data analysis (EDA) provides a set of statistical tools through which patterns in data may be extracted and examined in detail. The search space of EDA operations is enormous, too large to be explored directly in a data-driven manner. More abstract EDA procedures can be captured, however, by representations commonly used in AI planning systems. We describe an implemented planning representation for *Aide*, an automated EDA assistant, with a focus on control issues.

## Rational Interpolation for Rare Event Probabilities

### Stochastic Networks (1996-01-01) 117: 139-168 , January 01, 1996

We propose to use rational interpolants to tackle some computationally complex performance analysis problems such as rare-event probabilities in stochastic networks. Our main example is the computation of the cell loss probabilities in ATM multiplexers. The basic idea is to use the values of the performance function when the system size is small, together with the asymptotic behaviour when the size is very large, to obtain a rational interpolant which can be used for medium or large systems. This approach involves the asymptotic analysis of the rare-event probability as a function of the system size, the convergence analysis of rational interpolants on the positive real line, and the quasi-Monte Carlo analysis of discrete event simulation.

## A stopping rule for structure-preserving variable selection

### Statistics and Computing (1996-03-01) 6: 51-56 , March 01, 1996

A stopping rule is provided for the backward elimination process suggested by Krzanowski (1987a) for selecting variables to preserve data structure. The stopping rule is based on perturbation theory for Procrustes statistics, and a small simulation study verifies its suitability. Some illustrative examples are also provided and discussed.