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This paper presents a case study in the application of some statistical theory, and a mathematical model, to an actual business problem. The problem was to determine the pattern of mortality of subscriptions to a daily newspaper, and thereby to ascertain the average life of such subscriptions. The method of solution, herewith indicated, involved the collection of data from a probability sample of subscribers to the newspaper, and use of these data to construct a Markov chain. [ABSTRACT FROM AUTHOR]

Various methods based on Student t variates have been suggested and used for obtaining simultaneous confidence intervals for several means, or for several contrasts among means. Determination of an overall confidence level for such intervals involves evaluating the probability mass of a multivariate t distribution over a hypercube centered at the origin, with sides paralleling the coordinate planes, or obtaining bounds for this probability mass. Since such distributions involve many nuisance parameters, an impossible number of tables would be necessary in order to make exact confidence intervals. In the virtual absence of tables, approximations and bounds become important. In this paper, an attempt has been made to investigate the adequacy of certain suggested approximations [2], [5], [8] by computing the exact distributions for some particular cases. These exact distributions have been compared with approximations. This paper is concerned with two-sided confidence intervals, rather than one-sided intervals. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model for determining a minimum cost strategy for the following personnel recruiting and selection situation. A quota is set for the minimum number of good employees to be added each period, and selection is done on the basis of a test having a known correlation with the given criterion of job success. There is a total cost for all individuals recruited and a loss attached to each person hired who turns out to be unsatisfactory. The problem is to determine a minimum acceptable score on the selection test and the number of persons to be recruited which will yield a minimum cost, including loss, as well as satisfy the prescribed quota at a given probability level. [ABSTRACT FROM AUTHOR]

The decision-theoretic approach to point estimation involves the choice of an estimate to minimize the expected loss associated with the estimate. The purpose of this paper is to indicate the influence of risk aversion on point estimates for classes of payoff functions including the piecewise linear and quadratic payoff functions. Increased risk aversion results in a point estimate closer to zero for a quadratic pay. off function and a lower estimate with a piecewise linear payoff function, for example. [ABSTRACT FROM AUTHOR]

This paper derives a stochastic linear equation from factor analysis called factor analysis regression which is suggested as an alternative to classical least squares regression whenever least squares estimation is questionable or breaks down because of errors in the variables or multicollinearity. Statistical tests for the factor analysis regression are also suggested and an empirical example comparing factor-analysis regression with least squares is shown. [ABSTRACT FROM AUTHOR]

The mathematical models and methods of analysis of opposing forces, stemming from the original Lancaster equations are summarized in terms of two broad categories: (a) deterministic models, (b) stochastic models. The present limitations of previous methods are used to identify topics that require attention in the future. [ABSTRACT FROM AUTHOR]

The importance of adaptive and exponentially smoothed forecasting has led to the development of several schemes using the tracking signal or the smoothed auto correlation function for changing the value of the smoothing coefficient. An alternative scheme, using evolutionary spectra is proposed. The smoothing constant is determined as a function of the maximum change in the various frequency components of successive spectra. The location and magnitude of this maximum change also indicates the type of disturbance in the underlying stochastic process generating the series. Simulation experiments indicate that the use of spectra in this evolutionary fashion produces forecasts that are generally more stable as well as more sensitive to genuine changes than schemes based on the tracking signal. [ABSTRACT FROM AUTHOR]

A "blowup factor" is defined for the measurement of the effect on forecast error variance of two types of misspecification which may be implicit in the choice of a particular adaptive forecasting scheme: (1) misspecification of the number of non-zero parameters of the stationary linear stochastic process generating the observed time series, and (2) misspecification arising from postulating stationarity when in fact the generating process is non-stationary in mean. [ABSTRACT FROM AUTHOR]

In his paper, PEARCE presents a method for determining the stationary probabilities of a G/Mt/1 system, the service mechanism being such that it operates regardless of whether or not customers are present. This note is an attempt to correct his results. [ABSTRACT FROM AUTHOR]

A general method is developed for obtaining confidence limits on the mean of X+ Y where X and Yare two independent random variables whose individual distributions and percentiles are in standard statistical tables. The procedure uses this information to obtain approximations for the percentiles of the sum or approximate confidence limits on the mean of the sum. The method is applied to two problems: approximating the percentiles of the noncentral t distribution, and determining confidence limits for variance components in a one-way classification. Numerical examples compare it to other approximations. [ABSTRACT FROM AUTHOR]

A set of acts is specified. The decision maker can perform an experiment to learn more about his environment before he selects an act. Potential outcomes of each experiment are assumed to be known. Models are provided for determining optimal decision rules and an optimal experiment regardless of whether detailed consequences or states of the world have been formulated. [ABSTRACT FROM AUTHOR]

Any multistage process may be constructed by a sequence of serial and/or parallel compositions. With certain restrictions on the form of the return composition function, optimal processes may be constructed in an efficient manner from optimal subprocesses. A number of simple sufficient conditions on the return functions are given and several approximation procedures are outlined. [ABSTRACT FROM AUTHOR]

A complex system is to be placed in the field for a fixed period. During the period only the spares initially provided may be used to replace components that have failed Independence of failures is assumed among the essential components considered. Given the cost of components, the number of like components of each type simultaneously operating, the length of operation scheduled for each component, the failure distributions of components, a general mathematical solution is obtained for the composition of the spare parts kit which maximizes assurance of continued operation during the period, subject to a fixed budget for spares. Explicit formulas are obtained in the case of exponential failure distributions, constructive procedures in the case of monotone likelihood ratio densities. Fortunately, the identical mathematical model is applicable in determining the optimal allocation of redundancy in designing system reliability under a weight or cost restraint. [ABSTRACT FROM AUTHOR]

Techniques are derived for the estimation and testing of the effects on an intervention into a time-series. The time-series process postulated is a more general form of the integrated moving average model than for which estimation and testing procedures were formerly available. Application of the techniques to the analysis of data from a time-series experiment is illustrated. [ABSTRACT FROM AUTHOR]

The article examines the problem of estimating transition probabilities in Markov processes from a set of observations on one-dimensional frequency distributions. The author references the article "Least-Squares Estimates of Transition Probabilities," by L. G. Tesler to demonstrate an example presented therein of the market shares of three cigarette brands in the United States during the period 1925-1943. The solution to the equation is explored and solved under disregard of the inequality constraints.

Time series models of a complex nature, such as consumer brand switching analyses, have required assumptions of parameter stability because statistical models were not available to deal with parameter change. A model is developed here to estimate a stepwise change in the mean process of a Gaussian time series. Estimators which are small-sample efficient in a special sense are presented, along with examples and suggested applications of the method to brand switching problems. [ABSTRACT FROM AUTHOR]