Topic

# Negative binomial distribution

About: Negative binomial distribution is a(n) research topic. Over the lifetime, 4762 publication(s) have been published within this topic receiving 144255 citation(s).

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TL;DR: A method based on the negative binomial distribution, with variance and mean linked by local regression, is proposed and an implementation, DESeq, as an R/Bioconductor package is presented.

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Abstract: High-throughput sequencing assays such as RNA-Seq, ChIP-Seq or barcode counting provide quantitative readouts in the form of count data. To infer differential signal in such data correctly and with good statistical power, estimation of data variability throughout the dynamic range and a suitable error model are required. We propose a method based on the negative binomial distribution, with variance and mean linked by local regression and present an implementation, DESeq, as an R/Bioconductor package.

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11,332 citations

01 Jan 1950-

TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.

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Abstract: Office hours: MWF, immediately after class or early afternoon (time TBA). We will cover the mathematical foundations of probability theory. The basic terminology and concepts of probability theory include: random experiments, sample or outcome spaces (discrete and continuous case), events and their algebra, probability measures, conditional probability A First Course in Probability (8th ed.) by S. Ross. This is a lively text that covers the basic ideas of probability theory including those needed in statistics. Theoretical concepts are introduced via interesting concrete examples. In 394 I will begin my lectures with the basics of probability theory in Chapter 2. However, your first assignment is to review Chapter 1, which treats elementary counting methods. They are used in applications in Chapter 2. I expect to cover Chapters 2-5 plus portions of 6 and 7. You are encouraged to read ahead. In lectures I will not be able to cover every topic and example in Ross, and conversely, I may cover some topics/examples in lectures that are not treated in Ross. You will be responsible for all material in my lectures, assigned reading, and homework, including supplementary handouts if any.

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9,680 citations

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Abstract: Zero-inflated Poisson (ZIP) regression is a model for count data with excess zeros. It assumes that with probability p the only possible observation is 0, and with probability 1 – p, a Poisson(λ) random variable is observed. For example, when manufacturing equipment is properly aligned, defects may be nearly impossible. But when it is misaligned, defects may occur according to a Poisson(λ) distribution. Both the probability p of the perfect, zero defect state and the mean number of defects λ in the imperfect state may depend on covariates. Sometimes p and λ are unrelated; other times p is a simple function of λ such as p = l/(1 + λ T ) for an unknown constant T . In either case, ZIP regression models are easy to fit. The maximum likelihood estimates (MLE's) are approximately normal in large samples, and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the MLE's. Simulations suggest that the confidence intervals based on likelihood ratio test...

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3,205 citations

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01 Jan 2007-

Abstract: Preface 1. Introduction 2. The concept of risk 3. Overview of count response models 4. Methods of estimation and assessment 5. Assessment of count models 6. Poisson regression 7. Overdispersion 8. Negative binomial regression 9. Negative binomial regression: modeling 10. Alternative variance parameterizations 11. Problems with zero counts 12. Censored and truncated count models 13. Handling endogeneity and latent class models 14. Count panel models 15. Bayesian negative binomial models Appendix A. Constructing and interpreting interactions Appendix B. Data sets and Stata files References Index.

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2,774 citations

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TL;DR: It is shown that such a stochastic law is governed by the Beta Function, containing only one free parameter, and this is approximated by a skew or hyperbolic distribution of the type that is widespread in bibliometrics and diverse social science phenomena.

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Abstract: A Cumulative Advantage Distribution is proposed which models statistically the situation in which success breeds success. It differs from the Negative Binomial Distribution in that lack of success, being a non-event, is not punished by increased chance of failure. It is shown that such a stochastic law is governed by the Beta Function, containing only one free parameter, and this is approximated by a skew or hyperbolic distribution of the type that is widespread in bibliometrics and diverse social science phenomena. In particular, this is shown to be an appropriate underlying probabilistic theory for the Bradford Law, the Lotka Law, the Pareto and Zipf Distributions, and for all the empirical results of citation frequency analysis. As side results one may derive also the obsolescence factor for literature use. The Beta Function is peculiarly elegant for these manifold purposes because it yields both the actual and the cumulative distributions in simple form, and contains a limiting case of an inverse square law to which many empirical distributions conform.

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1,719 citations