Distributions of the ratio of two ranges of samples from nonnormal populations

The probability density function of the ratio of two ranges of samples from a population represented by an Edgeworth series is developed. The corrective functions arising due to nonnormality are tabulated for the upper 5 and 1 percent normal theory points and compared with those of F‐distribution. Indications are that both the variance ratio and the range ratio test are affected by nonnormality almost to the same extent. If there is any numerical difference for larger samples (say, n_:1 = n₂ >= 5), it is in the cases of symmetrical populations. The theoretical results are compared with those obtained from Monte Carlo sampling from x² and t‐distributions with various shape parameters.     

Some multiple decision problems in analysis of variance

In most practical situations to which the analysis of variance tests are applied, they do not supply the information that the experimenter aims at. If, for example, in one-way ANOVA the hypothesis is rejected in actual application of the F-test, the resulting conclusion that the true means θ₁,…,θ_k are not all equal, would by itself usually be insufficient to satisfy the experimenter. In fact his problems would begin at this stage. The experimenter may desire to select the “best” population or a subset of the “good” populations; he may like to rank the populations in order of “goodness” or he may like to draw some other inferences about the parameters of interest.

The extensive literature on selection and ranking procedures depends heavily on the use of independence between populations (block, treatments, etc.) in the analysis of variance. In practical applications, it is desirable to drop this assumption or independence and consider cases more general than the normal.

In the present paper, we derive a method to construct optimal (in some sense) selection procedures to select a nonempty subset of the k populations containing the best population as ranked in terms of θ_i’s which control the size of the selected subset and which maximizes the minimum average probability of selecting the best. We also consider the usual selection procedures in one-way ANOVA based on the generalized least squares estimates and apply the method to two-way layout case. Some examples are discussed and some results on comparisons with other procedures are also obtained.     

E-optimal block designs under heteroscedastic model

This paper mainly studies the E-optimality of block designs under a general heteroscedastic setting. The C-matrix of a block design under a heteroscedastic setting is obtained by using generalized least squares. Some bounds for the smallest positive eigenvalue of C-matrix are obtained in some general classes of connected designs. Use of these bounds is then made to obtain certain E-optimal block designs in various classes of connected block designs.     

Some tests with specified size for the behrens-fisher problem

For a given significance level α, Welch's approximate t-test for the Behrens-Fisher Problem is modified to get a test with size α. A useful result for carrying out the Berger and Boos test is provided. Simulation results give power comparisons of several size α tests.     

Hybrid censoring schemes with exponential failure distribution

The mixture of Type I and Type I1 censoring schemes, called the hybrid censoring, is quite important in life–testing experiments. Epstein(1954, 1960) introduced this testing scheme and proposed a two–sided confidence interval to estimate the mean lifetime, θ, when the underlying lifetime distribution is assumed to be exponential. There are some two–sided confidence intervals and credible intervals proposed by Fairbanks et al. (1982) and Draper and Guttman (1987) respectively. In this paper we obtain the exact two–sided confidence interval of θ following the approach of Chen and Bhattacharya (1988). We also obtain the asymptotic confidence intervals in the Hybrid censoring case. It is important to observe that the results for Type I and Type II censoring schemes can be obtained as particular cases of the Hybrid censoring scheme. We analyze one data set and compare different methods by Monte Carlo simulations.     

Determining Optimal Advertising Strategies: A Markov Decision Model Approach*

This study falls in the class of models in which advertising wearout and the differences between the learning and forgetting of advertisements are explicitly included. A discrete time Markov decision modeling approach is used to obtain optimal control limit policies, and an algorithm is provided to identify these policies. A control limit policy specifies whether or not to advertise in a specific time period on the basis of the level of awareness in that time period. Thus, the duration for which advertising is not done is determined endogenously, and the algorithm helps determine this duration for a given set of parameters. This is a particularly desirable feature, since advertising practitioners are interested in determining the optimal duration of advertising pulses. Computational experience suggests that the algorithm is very fast and easy to implement. Also, conditions on model parameters indicating the relative efficacy of pulsing versus uniform advertising are provided.     

Labour market integration of FRY refugees in Sweden vs. Denmark

We compare the long-run labour market integration of the Former Republic of Yugoslavia (FRY) refugees who arrived in the 1990s to the Scandinavian countries in the settings of Sweden and Denmark, respectively. These otherwise similar countries faced different economic conditions at the time of arrival and over the observation period. They also differed in terms of the restrictiveness of asylum policies and in attitudes towards immigration. Using register data from Statistics Sweden and Statistics Denmark, we show that FRY refugees, in both child and adult generations at arrival, are better integrated 12–15 years later in Sweden than in Denmark, even though Sweden experienced a higher level of unemployment than Denmark throughout the period. Our findings suggest that asylum policies promoting early labour market entry and early exposure to a host country's schooling system, as well as access to disability pension and social assistance, are important factors affecting refugee labour market integration.     

Martin K. Starr: A Visionary Proponent for System Integration,Modular Production,and Catastrophe Avoidance

Martin K. Starr facilitated the creation of an identity for production and operations management (POM) as an academic discipline. This paper aims to summarize Starr's substantial contributions to scholarly inquiry on system integration and interfunctional coordination, modular production, and catastrophe avoidance. Even after four decades, we describe how his legacy in these areas continues to define several major drivers of operations and supply chain management research and practice. Starr has influenced several generations of students, professors, and executives with his writings, teaching, and leadership roles in the POM community that include 32 years on the faculty of the Columbia School of Business, 15 years as Editor‐in‐Chief of Management Science, and presidency of the Production and Operations Management Society.