S. Zacks

Sequential Search of an Optimal Dosage, I

Abstract Sequential search procedures are described for determining an optimal dosage in the following biomedical problem. People are subjected to a certain chemotherapeutic treatment. The optimal dosage is the maximal dose for which the proportion of patients whose toxicity level does not cross the allowable limit is γ. We discuss Bayesian and non-Bayesian sequential procedures for searching the optimal dosage, assuming a linear regression between toxicity and dosage, and normal conditional distribution of the toxicity level at each dose, with a known variance.

Sequential Design for a Fixed Width Interval Estimation of the Common Mean of Two Normal Distributions. I. The Case of One Variance Known

Abstract The objective is to provide a fixed-width interval estimator of the unknown common mean of two normal distributions having a prescribed coverage probability and minimal possible sample size. The variance of one distribution is known. The design problem is to decide sequentially while sampling the distribution with the unknown variance when to switch and sample from the distribution with the known variance. New types of boundaries are derived for this sequential design problem. The operating characteristics of this procedure are compared with those of two other ad hoc procedures by Monte Carlo simulation.

Distribution of Adjusted Stock Levels under Statistical Adaptive Control Procedures of Inventory Systems

Abstract The article treats the problem of determining the probability distribution of adjusted stock levels K n+1(n = 0, 1, …), and of associated expected monthly cost, where is a sequence of i.i.d. random variable having an M.L.R. distribution (of monthly demand); is an adaptive estimator of the base stock level; and T n = Σ n i-1 X i . The recursive formulae for the determination of the probability distributions of K n+1 and of expected costs are developed. The exact computations are compared with an approximation based on the distribution of , and with Monte Carlo simulations.

Estimators of Severity Factors in a Multiplicative Poisson Model

Abstract Let Yij (i=1, …, li i=1, …, J) be independent Poisson random variables, with expectations λ= αiβji where Σαi = l. Such a model is called σ multiplicative Poisson; its factor parameters αi, are called severity factors, and β, are called intensity factors. The article concentrates on the problem of estimating the severity factors αi. Two types of estimators of αi are derived, Bayes and least-squares-maximum-likelihood. The expectations and mean square errors of these estimators are given and their relative efficiency is tabulated. The intensity factors β; are estimated from Ti = Σ Ii=1 yij, which are independent and have Poisson distributions with expectations θj = lβj, according to the common procedures.