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Some new statistical methods for a class of zerotruncated discrete distributions with applicationsDing, Xiqian, 丁茜茜 January 2015 (has links)
Counting data without zero category often occur in various _elds. Examples include days of hospital stay for patients, numbers of publication for tenuretracked faculty in a university, numbers of tra_c violation for drivers during a certain period and so on. A class of zerotruncated discrete models such as zerotruncated Poisson, zerotruncated binomial and zerotruncated negativebinomial distributions are proposed in literature to model such count data. In this thesis, firstly, literature review is presented in Chapter 1 on a class of commonly used univariate zerotruncated discrete distributions.
In Chapter 2, a unified method is proposed to derive the distribution of the sum of i.i.d. zerotruncated distribution random variables, which has important applications in the construction of the shortest ClopperPerson confidence intervals of parameters of interest and in the calculation of the exact pvalue of a twosided test for small sample sizes in one sample problem. These problems are discussed in Section 2.4. Then a novel expectationmaximization (EM) algorithm is developed for calculating the maximum likelihood estimates (MLEs) of parameters in general zerotruncated discrete distributions. An important feature of the proposed EM algorithm is that the latent variables and the observed variables are independent, which is unusual in general EMtype algorithms. In addition, a unified minorizationmaximization (MM) algorithm for obtaining the MLEs of parameters in a class of zerotruncated discrete distributions is provided.
The first objective of Chapter 3 is to propose the multivariate zerotruncated Charlier series (ZTCS) distribution by developing its important distributional properties, and providing efficient MLE methods via a novel data augmentation in the framework of the EM algorithm. Since the joint marginal distribution of any rdimensional subvector of the multivariate ZTCS random vector of dimension m is an rdimensional zerodeated Charlier series (ZDCS) distribution (1 6 r < m), it is the second objective of Chapter 3 to propose a new family of multivariate zeroadjusted Charlier series (ZACS) distributions (including the multivariate ZDCS distribution as a special member) with a more flexible correlation structure by accounting for both inflation and deflation at zero. The corresponding distributional properties are explored and the associated MLE method via EM algorithm is provided for analyzing correlated count data. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

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Useful methods for the distributions of products of random variablesBowser, Robert Dwight January 2010 (has links)
Digitized by Kansas Correctional Industries

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Distributionfree limits involving random variablesCho, TzeU January 2010 (has links)
Digitized by Kansas Correctional Industries

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On estimating the location parameter of the Cauchy distributionThomas, Richard Earl January 2010 (has links)
Digitized by Kansas Correctional Industries

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Distribution of the sum of independent unitytruncated logarithmic series variablesWayland, Russell James 01 May 1970 (has links)
Let X₁, X2, ••• , Xn be n independent and identically distributed random variables having the unitytruncated logarithmic series distribution with probability function given by f(x;0) = ᵅθX ⁄ x x ε T where α = [ log(1θ) θ ] 0 < θ < 1, and T = {2,3,…,∞}. Define their sum as Z = X₁ + X2 + … + Xn . We derive here the distribution of Z, denoted by p(z;n,θ), using the inversion formula for characteristic functions, in an explicit form in terms of a linear combination of Stirling numbers of the first kind. A recurrence relation for the probability function p(z;n,θ) is obtained and is utilized to provide a short table of pCz;n,8) for certain values of n and θ. Furthermore, some properties of p(z;n,θ) are investigated following Patil and Wani [Sankhla, Series A, 27, (1965), 27l280J.

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Contributions to statistical distribution theoryDavis, Arthur William January 1979 (has links)
1v. (various paging) : / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (D.Sc.)University of Adelaide, Dept. of Mathematical Sciences, 1981

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On the generalization of the distribution of the significant digits under computation /Wong, James Teng. January 1969 (has links)
Thesis (Ph. D.)Oregon State University, 1969. / Typescript. Includes bibliographical references (leaf 43). Also available on the World Wide Web.

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Inference problems based on noncentral distributionsVenables, W. N. (William N.) January 1971 (has links) (PDF)
Includes bibliographical references

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Application of the Gaussian model to a particulate emission control strategy evaluation problem /Doty, Edward James. January 1977 (has links)
Thesis (M.S.)Oregon Graduate Center, 1977.

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The distribution of Hotelling's generalized To².Hughes, David Timothy, January 1970 (has links)
ThesisUniversity of Florida. / Description based on print version record. Manuscript copy. Vita. Bibliography: leaves 117119.

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