Daniel Zelterman

Discrete Distributions (eBook, PDF)

Applications in the Health Sciences

• Format: PDF

Produktbeschreibung

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, although a good understanding of their properties is very important. 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.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 306
• Erscheinungstermin: 27. September 2005
• Englisch
• ISBN-13: 9780470868898
• Artikelnr.: 37299747

Autorenporträt

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.

Inhaltsangabe

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. 2.3.3 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. 6.6 Program for Exact Test of Homogeneity. 7 Sums of Dependent
Bernoulli's and Disease Clusters. 7.1 Introduction. 7.2 Conditional Models.
7.2.1 General results for conditional models. 7.2.2 Family history model.
7.2.3 Incremental risk model. 7.2.4 The exchangeable, beta-binomial
distribution. 7.2.5 Application to IPF example. 7.3 Exchangeable Models.
7.3.1 Exchangeable family history. 7.3.2 Exchangeable incremental risk
model. 7.4 Applications. 7.5 Appendix: Proof of Exchangeable Distribution.
8 Weighted Binomial Distributions and Disease Clusters. 8.1 Weighted Models
and Clustering. 8.2 The Altham Distribution. 8.3 Application to Childhood
Mortality Data. 8.4 A Log-linear Weighted Distribution. 8.5 Quadratic
Weighted Distributions. 8.6 Weighted Distributions in General. 8.7 Family
History Log-linear Model. 8.8 Summary Measures and IPF Example. 8.9 SAS
Program for Clustered Family Data. 9 Applications to Teratology
Experiments. 9.1 Introduction. 9.2 Dominant Lethal Assay. 9.3 Shell
Toxicology Experiment. 9.4 Toxicology of 2,4,5 T. Complements. References.
Index.

Rezensionen

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