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Title: On Some Contributions to Size Biased Probability Distributions
Researcher: Reshi Javaid Ahmad
Guide(s): Auqil Ahmad and Mir Khurshid Ahmad
Keywords: Beta Distributions
Exponential Distributions
Gamma Distributions
Probability Distributions
University: University of Kashmir
Completed Date: NA
Abstract: 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.
Pagination: NA
Appears in Departments:Department of Statistics

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02_certficate.pdf288.89 kBAdobe PDFView/Open
03_abstract.pdf150.91 kBAdobe PDFView/Open
04_acknowledgement.pdf139.29 kBAdobe PDFView/Open
05_contents.pdf153.99 kBAdobe PDFView/Open
06_chapter 1.pdf1.28 MBAdobe PDFView/Open
07_chapter 2.pdf1.12 MBAdobe PDFView/Open
08_chapter 3.pdf1.09 MBAdobe PDFView/Open
09_chapter 4.pdf545.37 kBAdobe PDFView/Open
10_chapter 5.pdf909.84 kBAdobe PDFView/Open
11_conclusion.pdf203.44 kBAdobe PDFView/Open
12_bibliography.pdf367.73 kBAdobe PDFView/Open

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