The Skew‐normal Distribution and Related Multivariate Families*

Abstract. This paper provides an introductory overview of a portion of distribution theory which is currently under intense development. The starting point of this topic has been the so‐called skew‐normal distribution, but the connected area is becoming increasingly broad, and its branches include now many extensions, such as the skew‐elliptical families, and some forms of semi‐parametric formulations, extending the relevance of the field much beyond the original theme of ‘skewness’. The final part of the paper illustrates connections with various areas of application, including selective sampling, models for compositional data, robust methods, some problems in econometrics, non‐linear time series, especially in connection with financial data, and more.     

Accounting for Both Random Errors and Systematic Errors in Uncertainty Propagation Analysis of Computer Models Involving Experimental Measurements with Monte Carlo Methods

A Monte Carlo method is presented to study the effect of systematic and random errors on computer models mainly dealing with experimental data. It is a common assumption in this type of models (linear and nonlinear regression, and nonregression computer models) involving experimental measurements that the error sources are mainly random and independent with no constant background errors (systematic errors). However, from comparisons of different experimental data sources evidence is often found of significant bias or calibration errors. The uncertainty analysis approach presented in this work is based on the analysis of cumulative probability distributions for output variables of the models involved taking into account the effect of both types of errors. The probability distributions are obtained by performing Monte Carlo simulation coupled with appropriate definitions for the random and systematic errors. The main objectives are to detect the error source with stochastic dominance on the uncertainty propagation and the combined effect on output variables of the models. The results from the case studies analyzed show that the approach is able to distinguish which error type has a more significant effect on the performance of the model. Also, it was found that systematic or calibration errors, if present, cannot be neglected in uncertainty analysis of models dependent on experimental measurements such as chemical and physical properties. The approach can be used to facilitate decision making in fields related to safety factors selection, modeling, experimental data measurement, and experimental design.     

Integration of Stochastic Effects and Data Uncertainties into the Design of Process Equipment

Stochastic effects and data uncertainties are present in any engineering calculation. Their impact may be particularly important if they concern the design of process equipment. A calculation model for the dynamic behavior of a heat exchanger and procedures to deal with the related uncertainties are presented. Their propagation through the calculation by means of a Monte Carlo approach is shown. The temperature at the heat exchanger outlet and the step response of a sudden variation in the heat exchanger inlet temperature are simulated and evaluated by way of example. It is demonstrated that the inclusion of stochastic effects and uncertainties provides a more reliable basis for design decisions and hence reduces the probability of errors.     

Parameter estimation in a verhulst stochastic model

Summary Maximum likelihood estimation is a well-known statistical tool. When applied to the study of dynamical continuous-time phenomena, it requires some specific assumptions. In this paper we discuss some properties of the maximum likelihood estimator for a stochastic Verhulst model and we show some simulation results on the behaviour of the corresponding discrete estimator.     

Technical Uncertainty in Quantitative Policy Analysis — A Sulfur Air Pollution Example

Expert judgments expressed as subjective probability distributions provide an appropriate means of incorporating technical uncertainty in some quantitative policy studies. Judgments and distributions obtained from several experts allow one to explore the extent to which the conclusions reached in such a study depend on which expert one talks to. For the case of sulfur air pollution from coal-fired power plants, estimates of sulfur mass balance as a function of plume flight time are shown to vary little across the range of opinions of leading atmospheric scientists while estimates of possible health impacts are shown to vary widely across the range of opinions of leading scientists in air pollution health effects.     

Optimal Prediction in Stochastic Regression Models with Application to the Analysis of Repeated Surveys

Several results relating to the optimal prediction of regression coefficients and random variables under a general linear model with stochastic coefficients are presented. These results are then applied to the analysis of repeated sample surveys over time. In particular, if the finite population can be modelled by a superpopulation model, a fully efficient method for the analysis of repeated surveys is proposed.     

随机Fuzzy子集理论初步

本文认为现行的Fuzzy子集理论有缺点,不能真实、准确地描述现实世界,因此有必要进行改进。我们将用随机Fuzzy子集理论中的随机隶属过程代替Fuzzy子集理论中的隶属函数,将客观世界中的确定性现象、随机现象和模糊现象结合起来进行研究。     

A case study in non-centering for data augmentation: Stochastic epidemics

In this paper, we introduce non-centered and partially non-centered MCMC algorithms for stochastic epidemic models. Centered algorithms previously considered in the literature perform adequately well for small data sets. However, due to the high dependence inherent in the models between the missing data and the parameters, the performance of the centered algorithms gets appreciably worse when larger data sets are considered. Therefore non-centered and partially non-centered algorithms are introduced and are shown to out perform the existing centered algorithms.     

Armitage-Doll Two-Stage Model: Implications and Extension

The objective of this paper is twofold: (1) to provide insight on the simplified MVK model of carcinogenesis (a model proposed by Moolgavkar and colleagues) by revealing the relationship between the Armitage-Doll two-stage model and the simplified MVK model; and (2) to extend the Armitage-Doll two-stage model to one with time-varying (piece-wise constant) parameters. It is shown that the simplified MVK model is a special case of the Armitage-Doll two-stage model, and many applications of the simplified MVK model involving intermittent exposures or exposures to different compounds in different time periods can be derived easily from the Armitage-Doll two-stage model with piece-wise constant parameters. The limitations of the Armitage-Doll two-stage model are discussed.     

Intelligent Procedures for Intra‐Day Updating of Call Center Agent Schedules

For nearly all call centers, agent schedules are typically created several days or weeks before the time that agents report to work. After schedules are created, call center resource managers receive additional information that can affect forecasted workload and resource availability. In particular, there is significant evidence, both among practitioners and in the research literature, suggesting that actual call arrival volumes early in a scheduling period (typically an individual day or week) can provide valuable information about the call arrival pattern later in the same scheduling period. In this paper, we develop a flexible and powerful heuristic framework for managers to make intra‐day resource adjustment decisions that take into account updated call forecasts, updated agent requirements, existing agent schedules, agents' schedule flexibility, and associated incremental labor costs. We demonstrate the value of this methodology in managing the trade‐off between labor costs and service levels to best meet variable rates of demand for service, using data from an actual call center.