1st Edition
Distributions for Modeling Location, Scale, and Shape Using GAMLSS in R
Part I: Parametric distributions and the GAMLSS family of distributions
Types of distributions
Properties of distributions
The GAMLSS Family of Distributions
Continuous distributions on (-8,8)
Continuous distributions on (0, 8)
Continuous distributions on (0, 1)
Discrete count distributions
Binomial type distributions
Mixed distributions
Part II: Advanced Topics
Statistical inference
Maximum likelihood estimation
Robustness of parameter estimation to outlier contamination
Methods of generating distributions
Discussion of skewness
Discussion of kurtosis
Skewness and kurtosis comparisons of continuous distributions
Heaviness of tails of distributions
Part III: Reference Guide
Continuous distributions on (-8,8)
Continuous distributions on (0, 8)
Mixed distributions on [0 to 8)
Continuous and mixed distributions on [0, 1]
Discrete count distributions
Binomial type distributions and multinomial distributions
Appendices
Biography
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.
"…focuses on all probability distributions that can be used in GAMLSS modelling…a distributional regression framework making inroads in different fields due to its flexibility…GAMLSS’s power rests on its capability to apply smoothers to numeric and categorical covariates and model numeric response variables via probability distributions other than the usual exponential family…including continuous　distributions, ...discrete distributions and mixtures of continuous and discrete (mixed) distributions...This last type of distribution, although commonplace in practice, is rather ignored by applied researchers…The book has three parts. Part II ("Advanced topics") contains eight Chapters, and is perhaps the most exciting section. It deals with topics that link the GAMLSS framework and probability distributions to ‘hot’ topics in statistical learning."
~ Fernando Marmolejo-Ramos, Raydonal Ospina, and Freddy Hernández-Barajas, respectively University of South Australia, Universidade Federal de Pernambuco, and Universidad Nacional de Colombia sede MedellÃn, appeared in Australian and New Zealand Journal of Statistics, September 2022
