Discrete Distributions - Applications in the Health Sciences

Informationen zum Autor Daniel Zelterman , PhD, is Professor of Epidemiology and Public Health, Division of Biostatistics, at Yale University. His application areas include work in AIDS and cancer. Before moving to Yale in 1995, he was on the faculty of the University of Minnesota and of the State University of New York at Albany. He is an elected Fellow of the American Statistical Association and is an Associate Editor of Biometrics and several other statistical journals. In his spare time, he plays the bassoon in several amateur chamber and orchestral groups in the New Haven area. Klappentext There have been many advances in the theory and applications of discrete distributions in recent years. They can be applied to a wide range of problems, particularly in the health sciences. Discrete Distributions: Applications in the Health Sciences describes a number of new discrete distributions that arise in the statistical examination of real examples. For each example, an understanding of the issues surrounding the data provides the motivation for the subsequent development of the statistical models. Provides an overview of discrete distributions and their applications in the health sciences. Focuses on real examples, giving readers an insight into the utility of the models. Describes the properties of each distribution, and the methods that led to their development. Presents a range of examples from the health sciences, including cancer, epidemiology, and demography. Features discussion of software implementation - in SAS, Fortran and R - enabling readers to apply the methods to their own problems. Written in an accessible style, suitable for applied statisticians and numerate health scientists. Software and data sets are made available on the Web. Discrete Distributions: Applications in the Health Sciences provides a practical introduction to these powerful statistical tools and their applications, suitable for researchers and graduate students from statistics and biostatistics. The focus on applications, and the accessible style of the book, make it an excellent practical reference source for practitioners from the health sciences. Zusammenfassung Discrete distributions are statistical models for counted data and are particularly applied in the health sciences. This book describes a collection of discrete distributions, emphasizing their applications while at the same time explaining the statistical methods and mathematical development. Inhaltsverzeichnis Preface. Acknowledgements. About the Author. 1 Introduction. 1.1 Discrete Distributions in General. 1.2 Multivariate Discrete Distributions. 1.3 Binomial Distribution. 1.4 The Multinomial Distribution. 1.5 Poisson Distribution. 1.6 Negative Binomial Distribution. 1.7 Hypergeometric Distribution. 1.7.1 Negative hypergeometric distribution. 1.7.2 Extended hypergeometric distribution. 1.8 Stirling's Approximation. 2 Maximum Negative Binomial Distribution. 2.1 Introduction. 2.1.1 Outfitting the ark. 2.1.2 Medical screening application. 2.2 Elementary Properties. 2.2.1 Shapes of the distribution. 2.2.2 Moments of the distribution. 2.2.3 Modes of the distribution. 2.3 Asymptotic Approximations. 2.3.1 Large values of c and p ¿ 1/2. 2.3.2 Large values of c and p ? 1/2. 2.3.3 Extreme values of p . 2.4 Estimation of p . 2.4.1 The likelihood function. 2.4.2 The EM estimate. 2.4.3 A Bayesian estimate of p . 2.5 Programs and Numerical Results. 2.6 Appendix: The Likelihood Kernel. 3 The Maximum Negative Hypergeometric Distribution. 3.1 Introduction. 3.2 The Distribution. 3.3 Properties and Approximati...

List of contents

Preface.
 
Acknowledgements.
 
About the Author.
 
1 Introduction.
 
1.1 Discrete Distributions in General.
 
1.2 Multivariate Discrete Distributions.
 
1.3 Binomial Distribution.
 
1.4 The Multinomial Distribution.
 
1.5 Poisson Distribution.
 
1.6 Negative Binomial Distribution.
 
1.7 Hypergeometric Distribution.
 
1.7.1 Negative hypergeometric distribution.
 
1.7.2 Extended hypergeometric distribution.
 
1.8 Stirling's Approximation.
 
2 Maximum Negative Binomial Distribution.
 
2.1 Introduction.
 
2.1.1 Outfitting the ark.
 
2.1.2 Medical screening application.
 
2.2 Elementary Properties.
 
2.2.1 Shapes of the distribution.
 
2.2.2 Moments of the distribution.
 
2.2.3 Modes of the distribution.
 
2.3 Asymptotic Approximations.
 
2.3.1 Large values of c and p <> 1/2.
 
2.3.2 Large values of c and p <> 1/2.
 
2.3.3 Extreme values of p.
 
2.4 Estimation of p.
 
2.4.1 The likelihood function.
 
2.4.2 The EM estimate.
 
2.4.3 A Bayesian estimate of p.
 
2.5 Programs and Numerical Results.
 
2.6 Appendix: The Likelihood Kernel.
 
3 The Maximum Negative Hypergeometric Distribution.
 
3.1 Introduction.
 
3.2 The Distribution.
 
3.3 Properties and Approximations.
 
3.3.1 Modes of the distribution.
 
3.3.2 A gamma approximation.
 
3.3.3 A half-normal approximation.
 
3.3.4 A normal approximation.
 
3.4 Estimation.
 
3.5 Appendix.
 
3.5.1 The half-normal approximation.
 
3.5.2 The normal approximate distribution.
 
4 Univariate Discrete Distributions for Use with Twins.
 
4.1 Introduction.
 
4.2 The Univariate Twins Distribution.
 
4.3 Measures of Association in Twins.
 
4.4 The Danish Twin Registry.
 
4.4.1 Estimate of the effect.
 
4.4.2 Approximations.
 
4.5 Appendix.
 
4.5.1 The univariate twins distribution.
 
4.5.2 Approximating distributions.
 
4.6 Programs for the Univariate Twins Distribution .
 
5 Multivariate Distributions for Twins.
 
5.1 Introduction.
 
5.2 Conditional Distributions.
 
5.2.1 Univariate conditional distribution.
 
5.2.2 Conditional association measure.
 
5.3 Conditional inference for the Danish twins.
 
5.4 Simultaneous Multivariate Distributions.
 
5.5 Multivariate Examination of the Twins.
 
5.6 Infinitesimal Multivariate Methods.
 
5.6.1 Models with no dependence.
 
5.6.2 Models for dependence.
 
5.6.3 The infinitesimal data.
 
5.7 Computer Programs.
 
5.7.1 Conditional distribution and association models in SAS.
 
5.7.2 Fortran program for multivariate inference.
 
6 Frequency Models for Family Disease Clusters.
 
6.1 Introduction.
 
6.1.1 Examples.
 
6.1.2 Sampling methods employed.
 
6.1.3 Incidence and clustering.
 
6.2 Exact Inference Under Homogeneous Risk.
 
6.2.1 Enumeration algorithm.
 
6.2.2 Ascertainment sampling.
 
6.3 Numerical Examples.
 
6.3.1 IPF in COPD families.
 
6.3.2 Childhood cancer syndrome.
 
6.3.3 Childhood mortality in Brazil.
 
6.3.4 Household T. cruzi infections.
 
6.4 Conclusions.
 
6.5 Appendix: Mathematical Details.
 
6.5.1 The distribution of family frequencies.
 
6.5.2 A model for covariates.
 
6.5.3 Ascertainment sampling.
&nb

Report

"...should appeal to those in statistical research and biostatistical practice who have similar applications." ( Technometrics , August 2005)

Product details

• Authors: D Zelterman, Daniel Zelterman, Daniel (Yale University Zelterman, Zelterman Daniel, Daniel Zeltermann
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 25.05.2004
• EAN: 9780470868881
• ISBN: 978-0-470-86888-1
• No. of pages: 312
• Series: Wiley Series in Probability and Statistics; Wiley Series in Probability and Statistics; Wiley Probability and Statisti
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Statistik, Regressionsanalyse, Statistics, Biostatistik, Multivariate Analyse, Biostatistics, Angew. Wahrscheinlichkeitsrechn. u. Statistik / Modelle, Applied Probability & Statistics - Models, Multivariate Analysis, Regression Analysis