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.     

Shortest paths among transient obstacles

Journal of Combinatorial Optimization - We present an optimal algorithm for determining a time-minimal rectilinear path among transient rectilinear obstacles. An obstacle is transient if it exists...     

Manufacturer–Retailer Negotiations in the Presence of an Oligopolistic Input Market

When a manufacturer relies solely on its own inputs in making products, the focus of negotiations between the manufacturer and retailer is exclusively on profits in the output (retail) market. In such cases, absent retail competition concerns, standard two‐part tariff negotiations set the per‐unit wholesale price equal to marginal cost, and require fixed transfers from the retailer to the manufacturer. In this article, we recognize that manufacturers often rely on imperfectly competitive markets for at least some inputs. Incorporating this seemingly natural feature has profound implications for manufacturer–retailer negotiations since it shifts their focus from being exclusively on output markets to one that balances strategic concerns in both input and output realms. The article's main result is that the added need to discipline input prices can lead the manufacturer and retailer to write contingent contracts that are cost‐plus and prescribe lump‐sum slotting allowances (i.e., fixed transfer from the manufacturer to the retailer).     

Tests for Serial Dependence and Other Specification Analysis in Models of Markets in Disequilibrium

The assumption of serial independence of disturbances is the starting point of most of the work done on analyzing market disequilibrium models. We derive tests for serial dependence given normality and homoscedasticity using the Lagrange multiplier (LM) test principle. Although the likelihood function under serial dependence is very complicated and involves multiple integrals of dimensions equal to the sample size, the test statistic we obtain through the LM principle is very simple. We apply the test to the housing-start data of Fair and Jaffee (1972) and study its finite sample properties through simulation. The test seems to perform quite well in finite samples in terms of size and power. We present an analysis of disequilibrium models that assumes that the disturbances are logistic rather than normal. The relative performances of these distributions are investigated by simulation.     

Quantile based reliability aspects of partial moments

Partial moments are extensively used in literature for modeling and analysis of lifetime data. In this paper, we study properties of partial moments using quantile functions. The quantile based measure determines the underlying distribution uniquely. We then characterize certain lifetime quantile function models. The proposed measure provides alternate definitions for ageing criteria. Finally, we explore the utility of the measure to compare the characteristics of two lifetime distributions.     

Characterization of Continuous Distributions by Variance Bound and Its Implications to Reliability Modeling and Catastrophe Theory

We generalize some of the existing results on characterization of continuous distributions by lower bound on the variance and point out their equivalence to characterization of life distributions by relationship between conditional expectation and failure (reversed failure) rate. It is shown that these lower bounds are the same as, Cramer–Rao bound in the regular case and improves upon the latter in the non-regular case. Some applications to reliability modeling and catastrophe theory are pointed out.     

On generalized hyper-Poisson distribution of order k and its application

ABSTRACT

Here we introduce a new class of distributions namely the generalized hyper-Poisson distribution of order k (GHPD(k)) as an order k version of the alpha-generalized hyper-Poisson distribution of Kumar and Nair (Statistica, 2014b Kumar, C.S., Nair, B.U. (2014b). A three parameter hyper-Poisson distribution and some of its properties. Statistica. 74(2):183–198. [Google Scholar]). Several properties of the GHPD(k) are derived and the estimation of the parameters of the distribution by the method of mixed moments and the method of maximum likelihood is discussed. Certain testing procedures are suggested and all these estimation and testing procedures are illustrated with the help of a real-life data set. Further a simulation study is conducted.     

Variable Royalty Rates for Improving Franchise Channel Coordination*

A business format franchisor obtains a major part of its revenues from franchise royalties, which are typically a fixed percentage of franchisee gross sales. When a fixed royalty rate is used and the marginal costs of operating the franchise are increasing, the franchisee does not have an incentive to increase sales beyond a certain “optimal” volume. We present a model that recommends the use of a variable franchise royalty rate for extending this optimal sales volume. For a general convex cost function, we show that a new lower rate can be applied to incremental sales beyond the original optimal level. We show that this new rate should be less than half of the original rate when a quadratic cost function is applicable. Adopting a variable royalty rate increases franchisor royalty revenues and franchisee profits.