# Confidence Interval Estimation for the Ratio of Binomial Proportions and Random Numbers Generation for Some Statistical Models

 dc.contributor.advisor Volodin, Andrei dc.contributor.author Ngamkham, Thuntida dc.date.accessioned 2018-11-15T21:02:00Z dc.date.available 2018-11-15T21:02:00Z dc.date.issued 2018-03 dc.identifier.uri http://hdl.handle.net/10294/8427 dc.description A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Statistics, University of Regina. xiii, 175 p. en_US dc.description.abstract A general problem of the interval estimation for a ratio of two proportions p1=p2 en_US according to data from two independent samples is considered. Each sample may be obtained in the framework of direct or inverse binomial sampling. Asymptotic confidence intervals are constructed in accordance with different types of sampling schemes with an application, where it is possible, of unbiased estimations of success probabilities and also their logarithms. Since methods of constructing confidence intervals in the situations when values for the both samples are obtained for identical sample schemes are already developed and well known, the main purpose of this paper is the investigation of constructing confidence intervals in two cases that correspond to different sampling schemes. In this situation it is possible to plan the sample size for the second sample according to the number of successes in the first sample. This, as it is shown by the results of statistical modeling, provides the intervals with confidence level which closer to the nominal value. Next, we provide a new procedure to generate random number that follow three parameter Crack distribution. To generate Crack random number by composition method, first we generate random number from already known two parameter distributions: Inverse Gaussian distribution, and Length Biased Inverse Gaussian distribution. Finally, we derive Crack random number generation procedure. Note that for many years the temperature and its temporal and spatial dynamics have been one of the determinants of demographic processes. The use of temperature values measured at the centre of population could significantly increase the accuracy of birth vs. temperature correlation analysis. Within the reported studies we have determined the center of population of the province of Saskatchewan of Canada. Unavailability of western-laboratory-type data on water quality for the areas where the aboriginal people live requires developing special evaluation and prognosis-making methodologies. To determine the key parameters of the water quality we interviewed the experts (aboriginal elders). Basing on the determined key parameters we formed the key questions and developed the questionnaires. The questionnaires were distributed among the households of the Peepeekisis and Kahkewistahaw aboriginal communities (Saskatchewan, Canada). dc.language.iso en en_US dc.publisher Faculty of Graduate Studies and Research, University of Regina en_US dc.title Confidence Interval Estimation for the Ratio of Binomial Proportions and Random Numbers Generation for Some Statistical Models en_US dc.type Thesis en dc.description.authorstatus Student en dc.description.peerreview yes en thesis.degree.name Doctor of Philosophy (PhD) en_US thesis.degree.level Doctoral en thesis.degree.discipline Statistics en_US thesis.degree.grantor University of Regina en thesis.degree.department Department of Mathematics and Statistics en_US dc.contributor.committeemember Yao, Yiyu dc.contributor.committeemember Deng, DianLiang dc.contributor.committeemember Sardarli, Arzu dc.contributor.externalexaminer Feng, Cindy Xin dc.identifier.tcnumber TC-SRU-8427 dc.identifier.thesisurl https://ourspace.uregina.ca/bitstream/handle/10294/8427/Ngamkham_Thuntida_PhD_STAT_Spring2018.pdf
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