05733nam 22007454a 450 991084157330332120170815122119.01-280-23879-897866102387980-470-34589-60-470-86890-20-470-86889-9(CKB)1000000000356019(EBL)239474(OCoLC)77722380(SSID)ssj0000139816(PQKBManifestationID)11134778(PQKBTitleCode)TC0000139816(PQKBWorkID)10028261(PQKB)10915058(MiAaPQ)EBC239474(PPN)19059781X(EXLCZ)99100000000035601920040128d2004 uy 0engur|n|---|||||txtccrDiscrete distributions[electronic resource] applications in the health sciences /Daniel ZeltermanHoboken, NJ John Wiley20041 online resource (307 p.)Wiley series in probability and statisticsDescription based upon print version of record.0-470-86888-0 Includes bibliographical references (p. 267-272) and index.Discrete Distributions; 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 Properties2.2.1 Shapes of the distribution2.2.2 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 approximation3.3.3 A half-normal approximation3.3.4 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 Twins5.1 Introduction5.2 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 Introduction6.1.1 Examples6.1.2 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 Clusters7.1 IntroductionThere 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.ProvidWiley series in probability and statistics.Medical sciencesMathematicsMedical sciencesMathematical modelsMedicineMathematicsDistribution (Probability theory)ProbabilitiesMedical sciencesMathematics.Medical sciencesMathematical models.MedicineMathematics.Distribution (Probability theory)Probabilities.519.24519.2402461610/.1/5118Zelterman Daniel144977MiAaPQMiAaPQMiAaPQBOOK9910841573303321Discrete distributions821076UNINA