Thesis (Ph. D.)--Carleton University, 1985. / Also available in electronic format on the Internet.

In this thesis the chance-constrained linear goal programming approach is developed to cover the following cases when the parameters have non-negative distributions: the exponential and the 'chi-square distributions. Case 1, when the right hand side coefficients are exponential or chi-square random vdriables. Case 2. when the input coefficients are exponential or chisquare random variables. The following have been achieved: For Case 1 1. We have developed a method for constructing deterministic linear goal programs equivalent to the original probabilistic linear goal programs. 2. We have given a probabilistic interpretation to the deviational random variables and the deviational random variable levels. For Case 2 We have developed a method for constructing deterministic nonlinear goal programs through the definition of the probabilistic deviational variables. 4. We have transformed the equivalent deterministic nonlinear goal programs into equivalent signomial goal programs. S. We have developed a computational algorithm for solving nonlinear goal programs generally and, more particularly, deterministic nonlinear goal programs equivalent to chance-constrained goal programs. iii 6. We have proved that Sengupta! s-transformation for obtaining deterministic programs equivalent to chanceconstrained programs does-not lead to solvable programs. 7. We have-formulated and solved a practical application - namely that of finding the "optimal distribution of exports and, imports to the marine, ports" using the methods and the algorithm presented in the thesis. The methods can be used when a program has mixed goals, some with right hand side coefficients or input coefficients that are exponential or chi-square random variables; -others, deterministic, that is without random variable parameters.

published_or_final_version / abstract / Computer Science / Master / Master of Philosophy

No description available.

Photocopy of typescript. / Digitized by Kansas Correctional Industries

Thesis (M. Phil.)--University of Hong Kong, 2008. / Also available in print.

abstract: It is common in the analysis of data to provide a goodness-of-fit test to assess the performance of a model. In the analysis of contingency tables, goodness-of-fit statistics are frequently employed when modeling social science, educational or psychological data where the interest is often directed at investigating the association among multi-categorical variables. Pearson's chi-squared statistic is well-known in goodness-of-fit testing, but it is sometimes considered to produce an omnibus test as it gives little guidance to the source of poor fit once the null hypothesis is rejected. However, its components can provide powerful directional tests. In this dissertation, orthogonal components are used to develop goodness-of-fit tests for models fit to the counts obtained from the cross-classification of multi-category dependent variables. Ordinal categories are assumed. Orthogonal components defined on marginals are obtained when analyzing multi-dimensional contingency tables through the use of the QR decomposition. A subset of these orthogonal components can be used to construct limited-information tests that allow one to identify the source of lack-of-fit and provide an increase in power compared to Pearson's test. These tests can address the adverse effects presented when data are sparse. The tests rely on the set of first- and second-order marginals jointly, the set of second-order marginals only, and the random forest method, a popular algorithm for modeling large complex data sets. The performance of these tests is compared to the likelihood ratio test as well as to tests based on orthogonal polynomial components. The derived goodness-of-fit tests are evaluated with studies for detecting two- and three-way associations that are not accounted for by a categorical variable factor model with a single latent variable. In addition the tests are used to investigate the case when the model misspecification involves parameter constraints for large and sparse contingency tables. The methodology proposed here is applied to data from the 38th round of the State Survey conducted by the Institute for Public Policy and Michigan State University Social Research (2005) . The results illustrate the use of the proposed techniques in the context of a sparse data set. / Dissertation/Thesis / Ph.D. Mathematics 2011

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaves 91-93. / by Mark Joseph Durst. / Ph.D.

Thesis (Ph. D.)--Oregon State University, 1981. / Typescript (photocopy). Includes bibliographical references (leaves 71-73). Also available via the World Wide Web.

The mystery of Canis Major overdensity is addressed. We discuss concurrent methods and their limitations on the determination of interstellar reddening. We establish a new way to determine line of sight interstellear reddening by observing stellar spectral lines and UBV colors. We observe and analyze spectra of 22 stars in different open clusters. We find that Hydrogen Balmer line at 4861 angstrom can predict the stellar atmospheric parameters and intrinsic colors with reasonable accuracy. Comparing with observed colors we derive the reddening of the stars. We compare our results with standard database WEBDA and find that within 90% probability limit the standard deviation of the error is 0.102798. This is improved by taking the absolute maximum probabilities and the scatter becomes 0.0688865.