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Statistical methods based on nonparametric and distribution-free procedures require the use of order statistics. Order statistics are also used in many parametric estimation and testing problems. With the introduction of modern high speed computers, order statistics have gained more importance in recent years in statistical inference - the main reason being that ranking a large number of observations manually was difficult and time consuming in the past, which is no longer the case at present because of the availability of high speed computers. Also, applications of order statistics require in many cases the use of numerical tables and computer is needed to construct these tables.In this thesis, some basic concepts and results involving order statistics are provided. Typically, application of the Theory of Permanents in the distribution of order statistics are discussed. Further, the correlation coefficient between the smallest observation (Y1) and the largest observation (Y,,) of a random sample of size n from two gamma populations, where (n-1) observations of the sample are from one population and the remaining observation is from the other population, is presented. / Department of Mathematical Sciences

This thesis reports an intervention informed by critical systems thinking. The intervention drew upon a variety of systems and operational research methods to systemically explore the problems facing housing services for older people. Stakeholders were then supported in developing a response to these problems in the form of an integrated model of user involvement and multi-agency working. The methods used in this study included Cognitive Mapping, Critical Systems Heuristics, Interactive Planning and Viable System Modelling. Following a description of the project and its outcomes, the author's practical experiences are used to reflect back on critical systems thinking. Five innovations are presented in the thesis: First a new method called 'Problem Mapping' is developed. This has five stages: (i) interviewing stakeholders to surface problems and identify further potential interviewees; (ii) listing the problems as seen through the eyes of the various stakeholders; (iii) consolidating the list by removing duplicate problems and synthesising similar problems into larger 'problem statements'; (iv) mapping the relationships between problems; and (v) presenting the results back to stakeholders to inform the development of proposals for improvement. Reflection upon the use of this method indicates that it is particularly valuable where there are multiple stakeholders who are not initially visible to researchers, each of whom sees different aspects of a problem situation. Second, Problem Mapping is used to systemically express the problems facing housing services for older people in two geographical areas in the UK. This shows how problems in the areas of assessment, information provision and planning are mutually reinforcing, making a strong case for change. Third, a process of evolving an integrated model of user involvement and multi-agency working is presented. The model was designed in facilitated workshops by managers from statutory agencies, based on specifications developed by a variety of stakeholders (including service users and carers). Fourth, the strengths and weaknesses of Cognitive Mapping (one of the methods used in the project) are discussed. Significant limitations of this method are highlighted. Fifth, contributions and reflections on the theoretical and practical basis of the research are presented. These among others focus on the theory of boundary critique, which is an important aspect of critical systems thinking. It is often assumed that boundary critique is only undertaken at the start of an intervention to ensure that its remit has been adequately defined. However, this project shows that it is both possible and desirable to use the theory of boundary critique in an on-going basis in interventions to inform the creative design of methods.

Thesis (M.S.)--Georgia Southern University, 2007. / "A thesis submitted to the Graduate Faculty of Georgia Southern University in partial fulfillment of the requirements for the degree Master of Science." Under the direction of Charles W. Champ. ETD. Electronic version approved: May 2007. Includes appendices.

Thesis (Ph. D.)--University of Washington. / Bibliography: l. 99-100.

Thesis (Ph.D.)--McMaster University, 2002. / Adviser: N. Balakrishnan. Includes bibliographical references. Also available via World Wide Web.