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This is the second volume in a series of books about using the GAMLSS R package developed by the authors. This volume presents a broad overview of statistical distributions and how they can be used in practical applications. It describes over 100 distributions - all available in the supporting R package - including their properties, limitations, and applications. Given the increasing size and complexity of available datasets, it is important to choose the underlying statistical distribution for your model very carefully, and this book gives both users and non-users of GAMLSS the tools to do that effectively.
Table of Contents
Part I: Parametric distributions and the GAMLSS family of distributions
Chapter 1 Types of distributions
Chapter 2 Properties of distributions
Chapter 3 The GAMLSS Family of Distributions
Chapter 4 Continuous distributions on (−1,1)
Chapter 5 Continuous distributions on (0, ∞)
Chapter 6 Continuous distributions on (0, 1)
Chapter 7 Discrete distributions for count data
Chapter 8 Binomial type distributions
Chapter 9 Mixed distributions
Part II: Advanced Topics
Chapter 10 Maximum likelihood
Chapter 11 Robustness of parameter estimation to outlier
Chapter 12 Methods of generating
Chapter 13 Discussion of skewness
Chapter 14 Discussion of Kurtosis
Chapter 15 Skewness and kurtosis comparisons of continuous distributions
Chapter 16 Heaviness of tails of continuous
Part III: Reference Guide
Chapter 17 Continuous distributions on (−∞,∞)
Chapter 18 Continuous distributions on (0, ∞)
Chapter 19 Mixed distributions on 0 to ∞, including 0
Chapter 20 Continuous and mixed distributions on [0, 1]
Chapter 21 Count data
Chapter 22 Binomial type data distributions
Robert Rigby was researching in Statistics at London Metropolitan University for over 30 years specializing in distributions and advanced regression and smoothing models (for supervised learning). He is one of the two original developers of GAMLSS models. He is currently a freelance consultant.
Mikis Stasinopoulos is a statistician. He has a considerable experience in applied statistics and he is one of the two creators of GAMLSS. He worked as the director of STORM, the statistics and mathematics research centre of London Metropolitan University and now he is working as an independent statistical consultant.
Gillian Heller is Professor of Statistics at Macquarie University, Sydney. Her research interests are mainly in flexible regression models for heavy-tailed count data, with applications in biostatistics and insurance.
Fernanda De Bastiani is a permanent lecturer in the Statistics Department at Universidade Federal de Pernambuco, Brazil. Her research interests are mainly in flexible regression models, spatial data analysis and influential diagnostics in regression models.
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