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Articles 1 - 3 of 3
Full-Text Articles in Probability
Exact Statistical Inferences For Functions Of Parameters Of The Log-Gamma Distribution, Joseph F. Mcdonald
Exact Statistical Inferences For Functions Of Parameters Of The Log-Gamma Distribution, Joseph F. Mcdonald
UNLV Theses, Dissertations, Professional Papers, and Capstones
The log-gamma model has been used extensively for flood frequency analysis and is an important distribution in reliability, medical and other areas of lifetime testing. Conventional methods fails to provide exact solutions for the log-gamma model while asymptotic methods provide approximate solutions that often have poor performance for typical sample sizes. The two parameter log-gamma distribution is examined using the generalized p-value approach. The methods are exact in the sense that the tests and the confidence intervals are based on exact probability statements rather than on asymptotic approximations. Exact tests and exact confidence intervals for the parameter of interest based …
A Gaming Application Of The Negative Hypergeometric Distribution, Steven Norman Jones
A Gaming Application Of The Negative Hypergeometric Distribution, Steven Norman Jones
UNLV Theses, Dissertations, Professional Papers, and Capstones
The Negative Hypergeometric distribution represents waiting times when drawing from a finite sample without replacement. It is analogous to the negative binomial, which models the distribution of waiting times when drawing with replacement. Even though the Negative Hypergeometric has applications it is typically omitted from textbooks on probability and statistics and is not generally known. The main purpose of this thesis is to derive expressions for the mean and variance of a new application of the Negative Hypergeometric to gaming and gambling. Other applications are described as well.
General Coupon Collecting Models And Multinomial Games, James Y. Lee
General Coupon Collecting Models And Multinomial Games, James Y. Lee
UNLV Theses, Dissertations, Professional Papers, and Capstones
The coupon collection problem is one of the most studied problems in statistics. It is the problem of collecting r (r<∞) distinct coupons one by one from k different kinds (k<∞) of coupons. We note that this is equivalent to the classical occupancy problem which involves the random allocation of r distinct balls into k distinct cells. Although the problem was first introduced centuries ago, it is still actively investigated today. Perhaps its greatest feature is its versatility, numerous approaches, and countless variations. For this reason, we are particularly interested in creating a classification system for the many generalizations of the coupon collection problem. In this thesis, we will introduce models that will be able to categorize these generalizations. In addition, we calculate the waiting time for the models under consideration. Our approach is to use the Dirichlet Type II integral. We compare our calculations to the ones obtained through Monte Carlo simulation. Our results will show that our models and the method used to find the waiting times are ideal for solving problems of this type.