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International Telemetering Conference Proceedings / October 26-29, 1998 / Town & Country Resort Hotel and Convention Center, San Diego, California / GPS signal fixed dwell and variable dwell time sequential search algorithms are compared with probability of false alarm and detection and searching rate. An adaptive search algorithm is proposed according to different work modes and interference or jam circumstance, which has effectively improved signal acquiring speed and reliability. Mathematical simulation shows its correction and feasible.

It is important to be able to compare variances efficiently and accurately regardless of the parent populations. This study proposes a new right tailed test for the ratio of two variances using the Edgeworth’s expansion. To study the Type I error rate and Power performance, simulation was performed on the new test with various combinations of symmetric and skewed distributions. It is found to have more controlled Type I error rates than the existing tests. Additionally, it also has sufficient power. Therefore, the newly derived test provides a good robust alternative to the already existing methods.

We study a natural generalization of the Λ-coalescent to a spatial continuum. We introduce the process, which is known as the Segregated Λ-coalescent, via its connections to the (non-spatial) Λ-coalescent and the Spatial Λ-Fleming-Viot process. The main new results contained in this thesis are as follows. The Segregated Λ-coalescent has a non-trivial construction which we present here in terms of stochastic flows. We describe the qualitative behaviour of the Segregated Λ-coalescent and compare it to the behaviour of the Λ-coalescent, showing in particular that the Segregated Λ-coalescent has an extra phase transition which is directly related to the introduction of space. We finish with some results concerning the rate at which the Segregated Λ-coalescent comes down from infinity.

Poker is a complex game to analyze. In this project we will use the mathematics of game theory to solve some simplified variations of the game. Probability is the building block behind game theory. We must understand a few concepts from probability such as distributions, expected value, variance, and enumeration methods to aid us in studying game theory. We will solve and analyze games through game theory by using different decision methods, decision trees, and the process of domination and simplification. Poker models, with and without cards, will be provided to illustrate optimal strategies. Extensions to those models will be presented, and we will show that optimal strategies still exist. Finally, we will close this paper with an original work to an extension that can be used as a medium to creating more extensions and, or, different games to explore.

This thesis suggests that the range of vocabulary in an individual’s lexicon has an influence on in their assessment of nonword wordlikeness. The study included thirteen Spanish-English bilinguals who participated in a language dominance questionnaire, standardized assessments of Spanish and English vocabulary knowledge, and Spanish and English wordlikeness judgment tasks. Resulting data demonstrated moderate correlations between vocabulary knowledge and performance on nonword wordlikeness judgement tasks in Spanish and English. Participants with larger lexicons appeared more tolerant of less probable nonwords, those with low phonotactic probability, while those with smaller lexicons were less accepting of nonwords with low phonotactic probability. The results suggest that an individual’s processing of low probability phonological constituents is influenced by the diversity and complexity of their linguistic knowledge and specifically, their vocabulary acquisition.

A well known result in probability is that convergence almost surely (a.s.) of a sequence of random elements implies weak convergence of their laws. The Ukrainian mathematician Anatoliy Volodymyrovych Skorohod proved the lemma known as Skorohods a.s. representation Theorem, a partial converse of this result. In this work we discuss the notion of continuous representations, which allows us to provide generalizations of Skorohods Theorem. In Chapter 2, we explore Blackwell and Dubinss extension [3] and Ferniques extension [10]. In Chapter 3 we present Cortissozs result [5], a variant of Skorokhods Theorem. It is shown that given a continuous path inM(S) it can be associated a continuous path with fixed endpoints in the space of S-valued random elements on a nonatomic probability space, endowed with the topology of convergence in probability. In Chapter 4 we modify Blackwell and Dubins representation for particular cases of S, such as certain subsets of R or R^n. / Mathematics

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Finding the distribution of a statistic is always an important problem that we face in statistical inference. Methods that are usually used for solving this problem are change of variable technique, distribution function technique and moment generating function technique. Among these methods change of variable technique is the most commonly used one. This method is simple when the statistic is a one-to-one transformation of the sample observations and if it is many-to-one, then one needs to compute the jacobian for each partition of the range for which the transformation is one-to-one. In addition, if we want to find the distribution of a statistic involving n random variables using the change of variable technique, we have to define (n-1) auxiliary variables. Unless these (n-1) auxiliary variables are carefully chosen, calculation of jacobian as well as finding the range of integration to obtain the marginal distribution of the statistic of interest become complicated. [See [3]]Au, Chi and Tam, Judy [1] proposed an alternative method of finding the distribution of a statistic by using Dirac generalized function. In this study we considera number of problems involving different probability distributions that are not quiet easy to solve by change of variable technique. We will illustrate the method by solving problems which include finding the distributions of sums, products, differences and ratios of random variables. The main purpose of the thesis is to show that using Dirac generalized function one can solve these problems with more ease. This alternative approach would be more suitable for students with limited mathematical background. / Department of Mathematical Sciences

Consider a probability distribution on the permutations of n elements. If the probability of each permutation is proportional to θK, where K is the number of cycles in the permutation, then we say that the distribution generates a θ-biased random permutation. A random permutation is a special θ-biased random permutation with θ = 1. The mth moment of the rth longest cycle of a random permutation is Θ(nm), regardless of r and θ. The joint moments are derived, and it is shown that the longest cycles of a permutation can either be positively or negatively correlated, depending on θ. The mth moments of the rth shortest cycle of a random permutation is Θ(nm−θ/(ln n)r−1) when θ < m, Θ((ln n)r) when θ = m, and Θ(1) when θ > m. The exponent of cycle lengths at the 100qth percentile goes to q with zero variance. The exponent of the expected cycle lengths at the 100qth percentile is at least q due to the Jensen’s inequality, and the exact value is derived.