Bivariate extreme value distributions

Let (X_i, Y_i), i = 1, 2,…, n, be n independent observations from a bivariate population and let X_(n) = max X_i and Y_(n) = max Y_i. This article gives a necessary and sufficient condition for the weak convergence of the distribution function of (X_(n), Y_(n)) to a nondegenerate distribution.     

Improving Right Party Contact Rates at Outbound Call Centers

Consumer delinquencies are a major problem for banks and other credit card issuers. These firms have collection centers across the country to collect outstanding balances from delinquent accounts. Their main strategy is to first send reminder notices and, if that does not work, to telephone delinquent customers and request payment. The latter often becomes necessary, resulting in high costs of collection. Automated dialers are used to make the calls, and when the call goes through, it is directed to one of several hundred associates manning computer workstations. In this operation, it is important to contact the account holder in order to discuss payment options. Simply getting someone on the line is not sufficient, because such calls would require follow‐up calls. The objective of efficient collections is to maximize dollars collected while minimizing costs, which generally translates to making a “right party contact (RPC)” in the minimum number of attempts. We developed and tested an algorithm that increased the RPC rates by over 10%. This increase translates to annual savings of several million dollars for an average credit card company. Although the focus of our paper is collections, the methodology developed is equally applicable for improving telemarketing efficiency.     

Coopetitive Buyer–Supplier Relationship: An Investigation of Bargaining Power,Relational Context,and Investment Strategies

This study proposes an analytical approach combined with a behavioral experiment for a joint examination of the competitive and cooperative (i.e., coopetitive) relationship between a buyer and a supplier. Specifically, the article considers the scenario in which the buyer and the supplier invest in strategic capabilities to increase their relative bargaining power. The article examines how dynamic investments in strategic assets are influenced by the locus of bargaining power and by the underlying context (synergistic vs. adversarial) of the interfirm relationship. The dynamic evolution of bargaining power is also examined. A dynamic game model is considered to examine the evolution of investment strategies in critical resources and to investigate the issues of bargaining power in a buyer–supplier dyad. Equilibrium expressions for the investment strategies of the buyer and the supplier are presented and their implications for buyer–supplier relationships are examined. The behavioral experiment complements the analytical model and examines the correspondence between optimal behavior suggested by the analytical model and the boundedly rational behavior of decision makers in an experimental context. The results from the model and behavioral experiments suggest that the strategies are a function of the risk‐adjusted returns obtained from investments. The experiment shows that, in a synergistic relational context when the buyer maintains bargaining power, the investment shifts of the buyer and the supplier accord well with theoretical predictions. In an adversarial relational context, the results of the experimental study do not correspond well with that predicted by the theoretical model. The implications of the results are discussed and directions for future research are presented.     

On determining the number of outliers in exponential and Pareto samples

In the present paper we suggest a procedure for the determination of the number of outliers in exponential and Pareto samples, using the predictive interval approach.     

Combining Judgmental and Statistical Forecasts: An Application to Earnings Forecasts

This study investigated the accuracy of combinations of statistical and judgmental forecasts of annual accounting earnings. Combined forecasts were generated as equally weighted (i.e., simple averages) and unequally weighted combinations of individual forecasts from time-series models of quarterly and annual earnings (statistical forecasts) and security analysts' forecasts of quarterly and annual earnings (judgmental forecasts). The effect of the number of individual forecasts combined on the accuracy of the combined forecasts was also examined. The empirical results indicated that, on the average, combined forecasts were more accurate than individual forecasts. The results also indicated that although analysts' forecasts are based on a wider information set, the accuracy of their forecasts could be improved by combining them with forecasts generated from statistical models. Even if the best individual forecast could be identified in advance, gains in accuracy could be achieved by using combinations of two other forecasting methods. Several of the combined forecasts were superior to the most accurate individual forecast. Forecasts combined by using unequal weights derived from a regression model proved more accurate than equally weighted combinations. Forecasting accuracy improved and the variability of accuracy across different combinations decreased as the number of forecasts in the combination increased.     

Some properties of discrete bathtub-shaped distributions

The existence and the usefulness of discrete bathtub-shaped and upside down bathtub-shaped distributions have been demonstrated in some papers of recent origin. However, the general properties of these two classes of distributions do not seem to have been discussed. This article proposes to study some reliability properties of such distributions. We investigate the closure properties with reference to convolution, mixing, series and parallel systems, etc. and existence of bounds on reliability functions, moment properties, and convergence.     

On some properties of equilibrium distributions of order n

In the present paper we derive some identities connecting the failure rate functions and moments of residual life of the nth order equilibrium distribution and the baseline distribution. These identities are used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution by relationships between various reliability characteristics. An approach using the characteristic functions is also discussed with illustrations.     

REDUCED RESIDUE CLASSES CYCLIC PBIB DESIGNS

A new general class of m-class cyclic association scheme is defined for v treatments, where v is a composite number. A simple method of construction of PBIB designs having this association scheme using more than one initial block and some methods using only one initial block are proposed. A complete analysis of this type of PBIB designs is given. Also given is a list of 39 useful PBIB designs of this type having v≤15 and r≤10 and having only three associate classes together with their efficiency factors for all types of comparisons and over all efficiency factors.     

An estimator of the common mean of two normal populations

In this paper we consider the estimation of the common mean of two normal populations when the variances are unknown. If it is known that one specified variance is smaller than the other, then it is possible to modify the Graybill-Deal estimator in order to obtain a more efficient estimator. One such estimator is proposed by Mehta and Gurland (1969). We prove that this estimator is more efficient than the Graybill-Deal estimator under the condition that one variance is known to be less than the other.