Download or read book Maximum Likelihood Estimation for a Class of Discrete Distributions written by G. E. (Gordon Ewart) Willmot and published by . This book was released on 1986 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Contributions to estimation in a class of discrete distributions Ganapati P Patil written by Ganapati P. Patil and published by . This book was released on 1959 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book CONTRIBUTIONS TO ESTIMATION IN A CLASS OF DISCRETE DISTRIBUTIONS written by GANAPATI PARASHURAM PATIL and published by . This book was released on 1959 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Adaptively Weighted Maximum Likelihood Estimation of Discrete Distributions written by Michael Amiguet and published by . This book was released on 2011 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Maximum Likelihood Estimation of Discrete Log Concave Distributions with Applications written by Yanhua Tian and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shape-constrained methods specify a class of distributions instead of a single parametric family. The approach increases the robustness of the estimation without much loss of efficiency. Among these, log-concavity is an appealing shape constraint in distribution modeling, because it falls into the popular unimodal shape-constraint and many parametric models are log-concave. This is, therefore, the focus of our work. First, we propose a maximum likelihood estimator of discrete log-concave distributions in higher dimensions. We define a new class of log-concave distributions in multiple dimensional spaces and study its properties. We show how to compute the maximum likelihood estimator from an independent and identically distributed sample, and establish consistency of the estimator, even if the class has been incorrectly specified. For finite sample sizes, the proposed estimator outperforms a purely nonparametric approach (the empirical distribution), but is able to remain comparable to the correct parametric approach. Furthermore, the new class has a natural relationship with log-concave densities when data has been grouped or discretized. We show how this property can be used in a real data example. Secondly, we apply the discrete log-concave maximum likelihood estimator in one-dimensional space to a clustering problem. Our work mainly focuses on the categorical nominal data. We develop a log-concave mixture model using the discrete log-concave maximum likelihood estimator. We then apply the log-concave mixture model to our clustering algorithm. We compare our proposed clustering algorithm with the other two clustering methods. Comparing results show that our proposed algorithm has a good performance.

Download or read book Discrete Distributions written by Norman L. Johnson and published by . This book was released on 1969 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Univariate Discrete Distributions written by Norman L. Johnson and published by John Wiley & Sons. This book was released on 2005-10-03 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Set Contains: Continuous Multivariate Distributions, Volume 1, Models and Applications, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 1, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 2, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discrete Multivariate Distributions by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Univariate Discrete Distributions, 3rd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discover the latest advances in discrete distributions theory The Third Edition of the critically acclaimed Univariate Discrete Distributions provides a self-contained, systematic treatment of the theory, derivation, and application of probability distributions for count data. Generalized zeta-function and q-series distributions have been added and are covered in detail. New families of distributions, including Lagrangian-type distributions, are integrated into this thoroughly revised and updated text. Additional applications of univariate discrete distributions are explored to demonstrate the flexibility of this powerful method. A thorough survey of recent statistical literature draws attention to many new distributions and results for the classical distributions. Approximately 450 new references along with several new sections are introduced to reflect the current literature and knowledge of discrete distributions. Beginning with mathematical, probability, and statistical fundamentals, the authors provide clear coverage of the key topics in the field, including: Families of discrete distributions Binomial distribution Poisson distribution Negative binomial distribution Hypergeometric distributions Logarithmic and Lagrangian distributions Mixture distributions Stopped-sum distributions Matching, occupancy, runs, and q-series distributions Parametric regression models and miscellanea Emphasis continues to be placed on the increasing relevance of Bayesian inference to discrete distribution, especially with regard to the binomial and Poisson distributions. New derivations of discrete distributions via stochastic processes and random walks are introduced without unnecessarily complex discussions of stochastic processes. Throughout the Third Edition, extensive information has been added to reflect the new role of computer-based applications. With its thorough coverage and balanced presentation of theory and application, this is an excellent and essential reference for statisticians and mathematicians.

Download or read book Finite Mixture Distributions written by B. Everitt and published by Springer. This book was released on 1981-05-28 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: General introduction; Mixtures of normal distributions; Mixtures of exponential and other continuous distributions; Mixtures of discrete distributions; Miscellaneous topics.

Download or read book Biases and Covariances of Maximum Likelihood Estimators written by Kimiko Osada Bowman and published by . This book was released on 1965 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Maximum Likelihood Estimation written by Scott R. Eliason and published by SAGE. This book was released on 1993 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a short introduction to Maximum Likelihood (ML) Estimation. It provides a general modeling framework that utilizes the tools of ML methods to outline a flexible modeling strategy that accommodates cases from the simplest linear models (such as the normal error regression model) to the most complex nonlinear models linking endogenous and exogenous variables with non-normal distributions. Using examples to illustrate the techniques of finding ML estimators and estimates, the author discusses what properties are desirable in an estimator, basic techniques for finding maximum likelihood solutions, the general form of the covariance matrix for ML estimates, the sampling distribution of ML estimators; the use of ML in the normal as well as other distributions, and some useful illustrations of likelihoods.

Download or read book Maximum Likelihood Estimation Based on Imcomplete Observations for a Class of Discrete Time Stochastic Processes by Means of the Kalman Filter written by Asger Roer Pedersen and published by . This book was released on 1993 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parameter Estimation and Other Aspects of Univariate and Bivariate Generalized Poisson Distributions written by J. A. Olapido and published by . This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Classical and Contagious Discrete Distributions written by Canadian Mathematical Congress and published by Calcutta : Statistical Pub. Society; distributed outside India by Pergamon Press, Oxford, New York. This book was released on 1965 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Competitive Tests and Estimators for Properties of Distributions written by Hirakendu Das and published by . This book was released on 2012 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive competitive tests and estimators for several properties of discrete distributions, based on their i.i.d. sequences. We focus on symmetric properties that depend only on the multiset of probability values in the distributions and not on specific symbols of the alphabet that assume these values. Many applications of probability estimation, statistics and machine learning involve such properties. Our method of probability estimation, called profile maximum likelihood (PML), involves maximizing the likelihood of observing the profile of the given sequences, i.e., the multiset of symbol counts in the sequences. It has been used successfully for universal compression of large alphabet data sources, and has been shown empirically to perform well for other probability estimation problems like classification and distribution multiset estimation. We provide competitive estimation guarantees for the PML method for several such problems. For testing closeness of distributions, i.e., finding whether two given i.i.d. sequences of length n are generated by the same distribution or by two different ones, our schemes have an error probability of at most sqrt(delta) * exp(7n^(2/3)) whenever the best possible error probability is delta = exp( -14n^(2/3)). The running time of our scheme is O(n). We do not make any assumptions on the distributions, including on their support size. In terms of sample complexity, this implies that if there is a closeness test which takes sequences of length n and has error probability at most delta, our tests have the same error guarantee on sequences of length n' = O(\max{n^3/log^3(1/4 delta), n}). Similar results are implied for the related problem of classification. For finding the probability multiset of a discrete distribution using a length-n i.i.d. sequence drawn from it, we show the following guarantee for the PML-based estimator. For any class of distributions and any distance metric on their probability multisets, if there is an estimator that approximates all distributions in this class to within a distance of epsilon 0 with error probability at most delta

Download or read book Maximum Likelihood Estimation Based on Incomplete Obeservations for a Class of Discrete Time Stochastic Processes by Means of the Kalman Filter written by Asger Roer Pedersen and published by . This book was released on 1993 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bivariate Discrete Distributions written by Kocherlakota and published by Routledge. This book was released on 2017-11-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This useful reference/text provides a comprehensive study of the various bivariate discretedistributions that have appeared in the literature- written in an accessible manner thatassumes no more than a first course in mathematical statistics.Supplying individualized treatment of topics while simultaneously exploiting the interrelationshipsof the material, Bivariate Discrete Distributions details the latest techniques ofcomputer simulation for the distributions considered ... contains a general introduction tothe structural properties of discrete distributions, including generating functions, momentrelationships, and the basic ideas of generalizing . . . develops distributions using samplingschemes . .. explores the role of compounding ... covers Waring and "short" distributionsfor use in accident theory ... discusses problems of statistical inference, emphasizing techniquespertinent to the discrete case ... and much more!Containing over 1000 helpful equations, Bivariate Discrete Distributions is