Statisticshttp://dspaces.uok.edu.in/jspui//handle/1/9722019-04-26T09:53:01Z2019-04-26T09:53:01ZOn some contributions to size-biased probability distributions.Reshi, Javaid Ahmad (Scholar)Aquil Ahmed (Guide)Mir, Khurshid Ahmad (Co-Guide)http://dspaces.uok.edu.in/jspui//handle/1/16912016-04-07T07:43:27Z2016-04-07T00:00:00ZOn some contributions to size-biased probability distributions.
Reshi, Javaid Ahmad (Scholar); Aquil Ahmed (Guide); Mir, Khurshid Ahmad (Co-Guide)
Statistical distributions and models are used in many applied areas such as economics, engineering, social, health and biological sciences. In this era of inexpensive and faster personnel computers, practitioners of statistics and scientists in various disciplines have no difficulty in fitting a probability model to describe the distributions of a real-life data set. Traditional enviromentric theory and practice have been occupied with randomization and replication. But in environmental and ecological work, observations also fall in the non-experimental, non-replicated and non-random catogries.The problems of model specification and data interpretation then acquire special importance and great concern. The theory of weighted distributions provides a unifying approach for these problems. Weighted distributions take into account the method of ascertainment, by adjusting the probabilities of actual occurrence of events to arrive at a specification of the probabilities of those events as observed and recorded. Failure to make such adjustments can lead to incorrect conclusions. The weighted distributions arise when the observations generated from a stochastic process are not given equal chance of being recorded; instead they are recorded according to some weight function. When the weight function depends on the lengths of the units of interest, the resulting distribution is called length biased. More generally, when the sampling mechanism selects units with probability proportional to some measure of the unit size, resulting distribution is called size-biased. Size-biased distributions are a special case of the more general form known as weighted distributions. These distributions arise in practice when observations from a sample are recorded with unequal probability. In Bayesian Statistics, the posterior distribution summarizes the current state of knowledge about all the uncertain quantities including unobservable parameters. In this thesis, the efforts have been made to study the areas.
Digital copy of Ph.D thesis
2016-04-07T00:00:00ZEntropy and information inequalities.Dar, Rayees Ahmad (Scholar)Baig, M. A. K. (Guide)http://dspaces.uok.edu.in/jspui//handle/1/16542016-01-19T08:48:56Z2016-01-19T00:00:00ZEntropy and information inequalities.
Dar, Rayees Ahmad (Scholar); Baig, M. A. K. (Guide)
The concept of information theory originated when an attempt was made to create a theoretical model for the transmission of information theory of various kinds. Information theory is a branch of mathematical theory of probability and is applied in wide variety of fields: communication theory, thermodynamics, econometrics, operation research and psychology etc. The development presented here have represented a step towards generalizing various measures of information, their characterization, application in coding theory and inference.
Digital copy of Thesis.
2016-01-19T00:00:00ZSome contributions to optimality criteria and duality in Multiobjective mathematical programming.Mattoo, Rumana Gulzar (Scholar)Aquil Ahmed (Guide)I. Husain (Co-Guide)http://dspaces.uok.edu.in/jspui//handle/1/16532016-01-19T08:42:07Z2016-01-19T00:00:00ZSome contributions to optimality criteria and duality in Multiobjective mathematical programming.
Mattoo, Rumana Gulzar (Scholar); Aquil Ahmed (Guide); I. Husain (Co-Guide)
This thesis entitled, “some contributions to optimality criteria and duality in multiobjective mathematical programming”, offers an extensive study on optimality, duality and mixed duality in a variety of multiobjective mathematical programming that includes nondifferentiable nonlinear programming, variational problems containing square roots of a certain quadratic forms and support functions which are prominent nondifferentiable convex functions. This thesis also deals with optimality, duality and mixed duality for differentiable and nondifferentiable variational problems involving higher order derivatives, and presents a close relationship between the results of continuous programming problems through the problems with natural boundary conditions between results of their counter parts in nonlinear programming. Finally it formulates a pair of mixed symmetric and self dual differentiable variational problems and gives the validation of various duality results under appropriate invexity and generalized invexity hypotheses. These results are further extended to a nondifferentiable case that involves support functions.
Digital copy of Thesis.
2016-01-19T00:00:00ZDuality in mathematical programming.Mashoob Masoodi (Scholar)Aquil Ahmed (Guide)I. Husain (Co-Guide)http://dspaces.uok.edu.in/jspui//handle/1/16522016-01-19T08:35:50Z2016-01-19T00:00:00ZDuality in mathematical programming.
Mashoob Masoodi (Scholar); Aquil Ahmed (Guide); I. Husain (Co-Guide)
In this thesis entitled, “Duality in Mathematical Programming”, the emphasis is given on formulation and conceptualization of the concepts of second-order duality, second-order mixed duality, second-order symmetric duality in a variety of nondifferentiable nonlinear programming under suitable second-order convexity/second-order invexity and generalized second-order convexity / generalized second-order invexity. Throughout the thesis nondifferentiablity occurs due to square root function and support functions. A support function which is more general than square root of a positive definite quadratic form. This thesis also addresses second-order duality in variational problems under suitable second-order invexity/secondorder generalized invexity. The duality results obtained for the variational problems are shown to be a dynamic generalization for thesis of nonlinear programming problem.
Digital copy of Thesis.
2016-01-19T00:00:00Z