An extension of the relaxation algorithm for solving a special case of capacitated arc routing problems

In this paper, we propose an exact method for solving a special integer program associated with the classical capacitated arc routing problems (CARPs) called split demand arc routing problems (SDARP). This method is developed in the context of monotropic programming theory and bases a promising foundation for developing specialized algorithms in order to solve general integer programming problems. In particular, the proposed algorithm generalizes the relaxation algorithm developed by Tseng and Bertsekas (Math. Oper. Res. 12(4):569–596, 1987) for solving linear programming problems. This method can also be viewed as an alternative for the subgradient method for solving Lagrangian relaxed problems. Computational experiments show its high potential in terms of efficiency and goodness of solutions on standard test problems.     

Cryptosporidiosis Susceptibility and Risk: A Case Study

Regional estimates of cryptosporidiosis risks from drinking water exposure were developed and validated, accounting for AIDS status and age. We constructed a model with probability distributions and point estimates representing Cryptosporidium in tap water, tap water consumed per day (exposure characterization); dose response, illness given infection, prolonged illness given illness; and three conditional probabilities describing the likelihood of case detection by active surveillance (health effects characterization). The model predictions were combined with population data to derive expected case numbers and incidence rates per 100,000 population, by age and AIDS status, borough specific and for New York City overall in 2000 (risk characterization). They were compared with same-year surveillance data to evaluate predictive ability, assumed to represent true incidence of waterborne cryptosporidiosis. The predicted mean risks, similar to previously published estimates for this region, overpredicted observed incidence-most extensively when accounting for AIDS status. The results suggest that overprediction may be due to conservative parameters applied to both non-AIDS and AIDS populations, and that biological differences for children need to be incorporated. Interpretations are limited by the unknown accuracy of available surveillance data, in addition to variability and uncertainty of model predictions. The model appears sensitive to geographical differences in AIDS prevalence. The use of surveillance data for validation and model parameters pertinent to susceptibility are discussed.     

Procrustes Shape Analysis of Planar Point Subsets

Consider a set of points in the plane randomly perturbed about a mean configuration by Gaussian errors. In this paper a Procrustes statistic based on the shapes of subsets of the points is studied, and its approximate distribution is found for small variations. We derive various properties of the distribution including the first two moments, a central limit result and a scaled χ²–-approximation. We concentrate on the independent isotropic Gaussian error case, although the results are valid for general covariance structures. We investigate triangle subsets in detail and in particular the situation where the population mean is regular (i.e. a Delaunay triangulation of the mean of the process is comprised of equilateral triangles of the same size). We examine the variance of the statistic for differently shaped regions and provide an asymptotic result for general shaped regions. The results are applied to an investigation of regularity in human muscle fibre cross-sections.     

Testing exponentiality based on Type-I censored data

The problem of goodness-of-fit for the exponential distribution when the available data are subject to Type-I censoring is discussed here. A test procedure is proposed in this case that exhibits more power as compared to existing methods. The power of the proposed test is assessed for several alternative distributions by means of Monte Carlo simulations. Finally, the proposed test is illustrated with a real data set.     

Efficiency of t-Test and Hotelling's T 2-Test After Box-Cox Transformation

Early investigations of the effects of non-normality indicated that skewness has a greater effect on the distribution of t-statistic than does kurtosis. When the distribution is skewed, the actual p-values can be larger than the values calculated from the t-tables. Transformation of data to normality has shown good results in the case of univariate t-test. In order to reduce the effect of skewness of the distribution on normal-based t-test, one can transform the data and perform the t-test on the transformed scale. This method is not only a remedy for satisfying the distributional assumption, but it also turns out that one can achieve greater efficiency of the test. We investigate the efficiency of tests after a Box-Cox transformation. In particular, we consider the one sample test of location and study the gains in efficiency for one-sample t-test following a Box-Cox transformation. Under some conditions, we prove that the asymptotic relative efficiency of transformed t-test and Hotelling's T ²-test of multivariate location with respect to the same statistic based on untransformed data is at least one.     

Estimation of the Parameters of a Two-phase Tandem Queue with a Second Optional Service

In this article, we consider a two-phase tandem queueing model with a second optional service. In this model, the service is done by two phases. The first phase of service is essential for all customers and after the completion of the first phase of service, any customer receives the second phase of service with probability α, or leaves the system with probability 1 ? α. Also, there are two heterogeneous servers which work independently, one of them providing the first phase of service and the other a second phase of service. In this model, our main purpose is to estimate the parameters of the model, traffic intensity, and mean system size, in the steady state, via maximum likelihood and Bayesian methods. Furthermore, we find asymptotic confidence intervals for mean system size. Finally, by a simulation study, we compute the confidence levels and mean length for asymptotic confidence intervals of mean system size with a nominal level 0.95.     

Testing the equality of correlation matrices

We present results that extend an existing test of equality of correlation matrices. A new test statistic is proposed and is shown to be asymptotically distributed as a linear combination of independent x ² random variables. This new formulation allows us to find the power of the existing test and our extensions by deriving the distribution under the alternative using a linear combination of independent non-central x ² random variables. We also investigate the null and the alternative distribution of two related statistics. The first one is a quadratic form in deviations from a control group with which the remaining k-1 groups are to be compared. The second test is designed for comparing adjacent groups. Several approximations for the null and the alternative distribution are considered and two illustrative examples are provided.     

Optimal design of the variable sampling size and sampling interval variable dimension T2 control chart for monitoring the mean vector of a multivariate normal process

This paper develops the algorithm for the optimization designs of the adaptive T² Control Chart for Monitoring the Mean Vector of a Multivariate Normal Process. It includes the variable sample size, variable sampling interval and variable dimensional chart. The VDT² control chart performs well for moderate and large shifts in the mean vector. However, its performance for small shifts is poor. To improve the chart's performance in detecting such shifts, we propose the application of the variable sample size and sampling interval technique to the VDT² control chart, resulting in the VSSIVDT² control chart.     

The frequency of sexual abuse and depression in a sample of street children of one of deprived districts of Tehran

The purpose of this study was to determine the frequency of sexual abuse and depression among street children who live in a deprived district of Tehran. The researchers used the K-SADS questionnaire and a clinical interview were used to evaluate depression and sexual abuse in 87 street children in Tehran. Eighteen (20.9%) of the children had been sexually abused. Depressed children were 3.2 times more likely to be sexually abused than non-depressed children. Furthermore, 26 girls (86.7%) and 27 boys (48.2%) suffered from depression. The frequency of depression demonstrated a significant association with the father's or breadwinner's history of imprisonment or unemployment. Interventional programs providing education and support should be implemented for street children.