Fisher, Nick; Lund, Robert; Osaki, Shunji; Polasek, Wolfgang; Tapiero, Charles; Teugels, Jef L.; Winkelmann, Rainer
1999 Applied Stochastic Models in Business and Industry
doi: 10.1002/(SICI)1526-4025(199904/06)15:2<87::AID-ASMB381>3.0.CO;2-Z
Williams, Christopher J.; Lee, Sauchi Stephen; Fisher, Rachel A.; Dickerman, Lois H.
1999 Applied Stochastic Models in Business and Industry
doi: 10.1002/(SICI)1526-4025(199904/06)15:2<89::AID-ASMB366>3.0.CO;2-K
Currently, prenatal screening for Down Syndrome (DS) uses the mother's age as well as three biochemical markers for risk prediction. Risk calculations for the biochemical markers use a quadratic discriminant function. In this paper we compare several classification procedures to quadratic discrimination methods for biochemical‐based DS risk prediction, based on data from a prospective multicentre prenatal screening study. We investigate alternative methods including linear discriminant methods, logistic regression methods, neural network methods, and classification and regression‐tree methods. Several experiments are performed, and in each experiment resampling methods are used to create training and testing data sets. The procedures on the test data set are summarized by the area under their receiver operating characteristic curves. In each experiment this process is repeated 500 times and then the classification procedures are compared. We find that several methods are superior to the currently used quadratic discriminant method for risk estimation for these data. The implications of these results for prenatal screening programs are discussed.
Stein, William E.; Dattero, Ronald
1999 Applied Stochastic Models in Business and Industry
doi: 10.1002/(SICI)1526-4025(199904/06)15:2<103::AID-ASMB369>3.0.CO;2-C
Bondesson's functions in reliability theory are shown to be related to a recursive sequence of probability distributions. These are the ‘higher‐order’ versions of the mean remaining lifetime in an equilibrium renewal process. Based on these functions, classes of distribution functions can be defined. This paper will investigate these classes and place Bondesson's work in the content of the other work done in reliability theory. Connections are made with the decreasing variance residual lifetime class and stochastic ordering. Copyright © 1999 John Wiley & Sons, Ltd.
Govil, Manish K.; Minis, Ioannis; Proth, Jean‐M.
1999 Applied Stochastic Models in Business and Industry
doi: 10.1002/(SICI)1526-4025(199904/06)15:2<111::AID-ASMB370>3.0.CO;2-0
This paper presents ways to predict the average queue length, at a manufacturing resource with a constant processing rate, at the time of a new lot arrival. The jobs arrive in constant lot sizes, and the inter arrival time of the lots follows an exponential distribution. Analytical expressions for the queue statistics are developed. Simulation results are provided and are compared to the theoretical predictions. Copyright © 1999 John Wiley & Sons, Ltd.
1999 Applied Stochastic Models in Business and Industry
doi: 10.1002/(SICI)1526-4025(199904/06)15:2<123::AID-ASMB371>3.0.CO;2-T
In this paper we point out the differences between the most common hazard‐based models, such as the proportional hazards and the accelerated failure time models. We focus on the heteroscestaticity‐across‐individuals problem that cannot be accommodated by them, and give motivation and general ideas about more flexible formulations. We describe hybrid and extended models, which have the former models as particular cases, but keep enough flexibility to fit data with heteroscedasticity. We show that by considering simple graphical procedures it is easy to verify whether there is heteroscedasticity in the data, whether it is possible to describe it through a simple function of the covariates, and whether it is important to take it in account for the final fit. Real datasets are considered. Copyright © 1999 John Wiley & Sons, Ltd.
1999 Applied Stochastic Models in Business and Industry
doi: 10.1002/(SICI)1526-4025(199904/06)15:2<131::AID-ASMB365>3.0.CO;2-H
In the context of a universe of trucks operating in the United States in 1990, this paper presents statistical methodology for estimating a finite universe total on a second occasion when a part of the universe is sampled and the remainder of the universe is not sampled. Prediction is used to compensate for the lack of data from the unsampled portion of the universe. The sample, stratified by age, is from an earlier census without updating the listing (frame). Accounting for births and deaths in the universe between the two points in time, an estimator is obtained which is a generalization of what an analyst might do in the absence of sample data from a given stratum, the births. Deaths are accounted for through domain estimation, and total updated counts are available from different sources. The approach of the paper is to provide an estimate for births, without actually sampling from the births stratum. With regard to saving resources by not sampling births, it is demonstrated that the analyst who does not sample the births may very well do better than the analyst who does. Copyright © 1999 John Wiley & Sons, Ltd.
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