عنوان

Dirichlet and Related Distributions

شابک

9780470688199 (hardback)

کد کشور

IR

شماره

E-6088

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

کشور محل نشر

IR

عنوان اصلي

Dirichlet and Related Distributions

نام عام مواد

[Book]

ساير اطلاعات عنواني

:Theory, Methods and Applications

نام نخستين پديدآور

/ Kai Wang Ng, Guo-Liang Tian, Man-Lai Tang

محل نشرو پخش و غیره

Hoboken, N.J.

نام ناشر، پخش کننده و غيره

: Wiley,

تاریخ نشرو بخش و غیره

, [2011], 2011.

نام خاص و کميت اثر

xxvi, 310 pages , 24 cm.

عنوان فروست

(Wiley Series in Probability and Statistics.)

متن يادداشت

Print

متن يادداشت

Includes bibliographical references (pages 289-302) and index.

متن يادداشت

8.1.3.Analyzing the crime survey data --8.1.4.Choice of an effective importance density --8.2.The hyper-Dirichlet distribution --8.2.1.Motivating examples --8.2.2.Density function --8.3.The scaled Dirichlet distribution --8.3.1.Two motivations --8.3.2.Stochastic representation and density function --8.3.3.Some properties --8.4.The mixed Dirichlet distribution --8.4.1.Density function --8.4.2.Stochastic representation --8.4.3.The moments --8.4.4.Marginal distributions --8.4.5.Conditional distributions --8.5.The Liouville distribution --8.6.The generalized Liouville distribution.

متن يادداشت

6.8.1.The likelihood ratio statistic and its null distribution --6.8.2.The C(a) test --6.8.3.Two illustrative examples --7.1.Density function --7.1.1.Definition --7.1.2.Truncated beta distribution --7.2.Motivating examples --7.2.1.Case A: matrix A is known --7.2.2.Case B: matrix A is unknown --7.2.3.Case C: matrix A is partially known --7.3.Conditional sampling method --7.3.1.Consistent convex polyhedra --7.3.2.Marginal distributions --7.3.3.Conditional distributions --7.3.4.Generation of random vector from a truncated Dirichlet distribution --7.4.Gibbs sampling method --7.5.The constrained maximum likelihood estimates --7.6.Application to misclassification --7.6.1.Screening test with binary misclassifications --7.6.2.Case[-]control matched-pair data with polytomous misclassifications --7.7.Application to uniform design of experiment with mixtures --8.1.The generalized Dirichlet distribution --8.1.1.Density function --8.1.2.Statistical inferences.

متن يادداشت

5.8.Applications --5.8.1.Bayesian analysis of variance in a linear model --5.8.2.Confidence regions for variance ratios in a linear model with random effects --6.1.Probability mass function --6.1.1.Motivation --6.1.2.Definition via a mixture representation --6.1.3.Beta-binomial distribution --6.2.Moments of the distribution --6.3.Marginal and conditional distributions --6.3.1.Marginal distributions --6.3.2.Conditional distributions --6.3.3.Multiple regression --6.4.Conditional sampling method --6.5.The method of moments estimation --6.5.1.Observations and notations --6.5.2.The traditional moments method --6.5.3.Mosimann's moments method --6.6.The method of maximum likelihood estimation --6.6.1.The Newton[-]Raphson algorithm --6.6.2.The Fisher scoring algorithm --6.6.3.The EM gradient algorithm --6.7.Applications --6.7.1.The forest pollen data --6.7.2.The teratogenesis data --6.8.Testing the multinomial assumption against the Dirichlet[-]multinomial alternative.

متن يادداشت

5.1.1.Density function --5.1.2.Several useful integral formulae --5.1.3.The mixed moment and the mode --5.2.Definition through stochastic representation --5.3.Marginal and conditional distributions --5.4.Cumulative distribution function and survival function --5.4.1.Cumulative distribution function --5.4.2.Survival function --5.5.Characteristic function --5.5.1.Univariate case --5.5.2.The confluent hypergeometric function of the second kind --5.5.3.General case --5.6.Distribution for linear function of inverted Dirichlet vector --5.6.1.Introduction --5.6.2.The distribution of the sum of independent gamma variates --5.6.3.The case of two dimensions --5.7.Connection with other multivariate distributions --5.7.1.Connection with the multivariate t distribution --5.7.2.Connection with the multivariate logistic distribution --5.7.3.Connection with the multivariate Pareto distribution --5.7.4.Connection with the multivariate Cook-Johnson distribution.

متن يادداشت

4.3.Stochastic representation, mixed moments, and mode --4.4.Marginal distributions --4.5.Conditional distributions --4.6.Connection with exact null distribution for sphericity test --4.7.Large-sample likelihood inference --4.7.1.Likelihood with NDD form --4.7.2.Likelihood beyond NDD form --4.7.3.Comparison with existing likelihood strategies --4.8.Small-sample Bayesian inference --4.8.1.Likelihood with NDD form --4.8.2.Likelihood beyond NDD form --4.8.3.Comparison with the existing Bayesian strategy --4.9.Applications --4.9.1.Sample surveys with nonresponse: simulated data --4.9.2.Dental caries data --4.9.3.Competing-risks model: failure data for radio transmitter receivers --4.9.4.Sample surveys: two data sets for death penalty attitude --4.9.5.Bayesian analysis of the ultrasound rating data --4.10.A brief historical review --4.10.1.The neutrality principle --4.10.2.The short memory property --5.1.Definition through the density function.

متن يادداشت

3.2.Density function --3.3.Basic properties --3.4.Marginal distributions --3.5.Conditional distributions --3.6.Extension to multiple partitions --3.6.1.Density function --3.6.2.Some properties --3.6.3.Marginal distributions --3.6.4.Conditional distributions --3.7.Statistical inferences: likelihood function with GDD form --3.7.1.Large-sample likelihood inference --3.7.2.Small-sample Bayesian inference --3.7.3.Analyzing the cervical cancer data --3.7.4.Analyzing the leprosy survey data --3.8.Statistical inferences: likelihood function beyond GDD form --3.8.1.Incomplete 2 2 contingency tables: the neurological complication data --3.8.2.Incomplete r c contingency tables --3.8.3.Wheeze study in six cities --3.8.4.Discussion --3.9.Applications under nonignorable missing data mechanism --3.9.1.Incomplete r c tables: nonignorable missing mechanism --3.9.2.Analyzing the crime survey data --4.1.Density function --4.2.Two motivating examples.

متن يادداشت

2.6.Characterizations --2.6.1.Mosimann's characterization --2.6.2.Darroch and Ratcliff's characterization --2.6.3.Characterization through neutrality --2.6.4.Characterization through complete neutrality --2.6.5.Characterization through global and local parameter independence --2.7.MLEs of the Dirichlet parameters --2.7.1.MLE via the Newton-Raphson algorithm --2.7.2.MLE via the EM gradient algorithm --2.7.3.Analyzing serum-protein data of Pekin ducklings --2.8.Generalized method of moments estimation --2.8.1.Method of moments estimation --2.8.2.Generalized method of moments estimation --2.9.Estimation based on linear models --2.9.1.Preliminaries --2.9.2.Estimation based on individual linear models --2.9.3.Estimation based on the overall linear model --2.10.Application in estimating ROC area --2.10.1.The ROC curve --2.10.2.The ROC area --2.10.3.Computing the posterior density of the ROC area --2.10.4.Analyzing the mammogram data of breast cancer --3.1.Three motivating examples.

متن يادداشت

1.7.4.Sampling issues in Bayesian MDPs --1.8.Basic statistical distributions --1.8.1.Discrete distributions --1.8.2.Continuous distributions --2.1.Definition and basic properties --2.1.1.Density function and moments --2.1.2.Stochastic representations and mode --2.2.Marginal and conditional distributions --2.3.Survival function and cumulative distribution function --2.3.1.Survival function --2.3.2.Cumulative distribution function --2.4.Characteristic functions --2.4.1.The characteristic function of u approximately = U(Tn) --2.4.2.The characteristic function of v approximately = U(Vn) --2.4.3.The characteristic function of a Dirichlet random vector --2.5.Distribution for linear function of a Dirichlet random vector --2.5.1.Density for linear function of v approximately = U(Vn) --2.5.2.Density for linear function of u approximately = U(Tn) --2.5.3.A unified approach to linear functions of variables and order statistics --2.5.4.Cumulative distribution function for linear function of a Dirichlet random vector.

متن يادداشت

Machine generated contents note:1.1.Motivating examples --1.2.Stochastic representation and the = operator --1.2.1.Definition of stochastic representation --1.2.2.More properties on the = operator --1.3.Beta and inverted beta distributions --1.4.Some useful identities and integral formulae --1.4.1.Partial-fraction expansion --1.4.2.Cambanis[-]Keener[-]Simons integral formulae --1.4.3.Hermite[-]Genocchi integral formula --1.5.The Newton[-]Raphson algorithm --1.6.Likelihood in missing-data problems --1.6.1.Missing-data mechanism --1.6.2.The expectation[-]maximization (EM) algorithm --1.6.3.The expectation/conditional maximization (ECM) algorithm --1.6.4.The EM gradient algorithm --1.7.Bayesian MDPs and inversion of Bayes' formula --1.7.1.The data augmentation (DA) algorithm --1.7.2.True nature of Bayesian MDP: inversion of Bayes' formula --1.7.3.Explicit solution to the DA integral equation.

متن يادداشت

"This book provides a comprehensive review on the Dirichlet distribution including its basic properties, marginal and conditional distributions, cumulative distribution and survival functions. The authors provide insight into new materials such as survival function, characteristic functions for two uniform distributions over the hyper-plane and simplex distribution for linear function of Dirichlet components estimation via the expectation-maximization gradient algorithm and application. Two new families of distributions (GDD and NDD) are explored, with emphasis on applications in incomplete categorical data and survey data with non-response. Theoretical results on inverted Dirichlet distribution and its applications are featured along with new results that deal with truncated Dirichlet distribution, Dirichlet process and smoothed Dirichlet distribution. The final chapters look at results gathered for Dirichlet-multinomial distribution, Generalized Dirichlet distribution, Liouville distribution, generalized Liouville distribution and matrix-variate Dirichlet distribution"--Provided by publisher.

عنوان

Wiley series in probability and statistics

موضوع مستند نشده

Distribution (Probability theory)

موضوع مستند نشده

Dirichlet problem

شماره

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Ng, Kai Wang,author.

مستند نام اشخاص تاييد نشده

Tian, Guo-Liang,author

مستند نام اشخاص تاييد نشده

Tang, Man-Lai,author

کشور

ایران

وضعیت فهرست نویسی

old catalog

فرمت انتشار

p

نوع ماده

BL

پیشوند ISBD اعمال شده است

1

سطح دسترسي

a

تكميل شده

Y