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Book Maximum Likelihood Estimation for a Class of Multinomial Distributions Arising in Reliability

Download or read book Maximum Likelihood Estimation for a Class of Multinomial Distributions Arising in Reliability written by F. J. Samaniego and published by . This book was released on 1978 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let X sub i, i=1, ..., k be independent Bernoulli random variables with potentially different probabilities of success p sub i, i-1, ..., k. This situation is denoted by X sub i approx B(1,pi), i=1, ..., k. Let Y = sub over i = 1 to k of X sub i and assume that a random sample Y1, Y2 ..., Yn is available. The common distribution of these Y's is the k-fold convolution to be denoted *(i = 1 to k). This note concerns the estimation of the parameters of this convolution based on the Y sample via the method of maximum likelihood.

Book Final Report Grant AFOSR 77 3180

Download or read book Final Report Grant AFOSR 77 3180 written by F. J. Samaniego and published by . This book was released on 1981 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report summarizes research progress under the grant in the following areas: a characterization of convoluted geometric distributions; a generalization of a theorem by Boswell and Patil; maximum likelihood estimation for binomially distributed signals in discrete noise; on the power of the X sq goodness of fit test at signal plus noise alternatives; two characterizations for Pascal signals in additive noise; maximum likelihood estimation for a class of multinomial distributions arising in reliability; pseudo maximum likelihood estimation: theory and applications; bathtub and related failure rate characterizations; a unified treatment of modeling and inference for discrete signals in additive noise; statistical inference for a new model in reliability; modeling and inference for positively dependent variables in dichotomous experiments; maximum likelihood estimation for a discrete multivariate shock model; moment identities via integrated survival curves; evaluating performance in continuous experiments with feedback to subjects; estimating the sib proportion in seed purity determinations; and estimating a survival curve when new is better than used. (Author).

Book Maximum Likelihood Estimation of Parameters with Constraints in Normal and Multinomial Distributions

Download or read book Maximum Likelihood Estimation of Parameters with Constraints in Normal and Multinomial Distributions written by HUITIAN. XUE and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Maximum Likelihood Estimation of Parameters With Constraints in Normal and Multinomial Distributions" by Huitian, Xue, 薛惠天, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Motivated by problems in medicine, biology, engineering and economics, con- strained parameter problems arise in a wide variety of applications. Among them the application to the dose-response of a certain drug in development has attracted much interest. To investigate such a relationship, we often need to conduct a dose- response experiment with multiple groups associated with multiple dose levels of the drug. The dose-response relationship can be modeled by a shape-restricted normal regression. We develop an iterative two-step ascent algorithm to estimate normal means and variances subject to simultaneous constraints. Each iteration consists of two parts: an expectation{maximization (EM) algorithm that is utilized in Step 1 to compute the maximum likelihood estimates (MLEs) of the restricted means when variances are given, and a newly developed restricted De Pierro algorithm that is used in Step 2 to find the MLEs of the restricted variances when means are given. These constraints include the simple order, tree order, umbrella order, and so on. A bootstrap approach is provided to calculate standard errors of the restricted MLEs. Applications to the analysis of two real datasets on radioim-munological assay of cortisol and bioassay of peptides are presented to illustrate the proposed methods. Liu (2000) discussed the maximum likelihood estimation and Bayesian estimation in a multinomial model with simplex constraints by formulating this constrained parameter problem into an unconstrained parameter problem in the framework of missing data. To utilize the EM and data augmentation (DA) algorithms, he introduced latent variables {Zil;Yil} (to be defined later). However, the proposed DA algorithm in his paper did not provide the necessary individual conditional distributions of Yil given (the observed data and) the updated parameter estimates. Indeed, the EM algorithm developed in his paper is based on the assumption that{ Yil} are fixed given values. Fortunately, the EM algorithm is invariant under any choice of the value of Yil, so the final result is always correct. We have derived the aforesaid conditional distributions and hence provide a valid DA algorithm. A real data set is used for illustration. DOI: 10.5353/th_b4785001 Subjects: Estimation theory Parameter estimation

Book Maximum Likelihood Estimation for Sample Surveys

Download or read book Maximum Likelihood Estimation for Sample Surveys written by Raymond L. Chambers and published by CRC Press. This book was released on 2012-05-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample surveys provide data used by researchers in a large range of disciplines to analyze important relationships using well-established and widely used likelihood methods. The methods used to select samples often result in the sample differing in important ways from the target population and standard application of likelihood methods can lead to

Book Quality Control and Applied Statistics

Download or read book Quality Control and Applied Statistics written by and published by . This book was released on 1982 with total page 1210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Statistical Theory and Method Abstracts

Download or read book Statistical Theory and Method Abstracts written by and published by . This book was released on 2001 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Biased Sampling Over identified Parameter Problems and Beyond

Download or read book Biased Sampling Over identified Parameter Problems and Beyond written by Jing Qin and published by Springer. This book was released on 2017-06-14 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to biased sampling problems (also called choice-based sampling in Econometrics parlance) and over-identified parameter estimation problems. Biased sampling problems appear in many areas of research, including Medicine, Epidemiology and Public Health, the Social Sciences and Economics. The book addresses a range of important topics, including case and control studies, causal inference, missing data problems, meta-analysis, renewal process and length biased sampling problems, capture and recapture problems, case cohort studies, exponential tilting genetic mixture models etc. The goal of this book is to make it easier for Ph. D students and new researchers to get started in this research area. It will be of interest to all those who work in the health, biological, social and physical sciences, as well as those who are interested in survey methodology and other areas of statistical science, among others.

Book Rates of Convergence for Estimation and Testing in Multinomial Distributions

Download or read book Rates of Convergence for Estimation and Testing in Multinomial Distributions written by Kenneth Henry Sutrick and published by . This book was released on 1979 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Maximum Likelihood Estimation of the Multinomial Dirichlet Distribution

Download or read book Maximum Likelihood Estimation of the Multinomial Dirichlet Distribution written by Manohar U. Kalwani and published by . This book was released on 1980 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: