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      Book

      Distributions for Modeling Location, Scale, and Shape
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      Book

      Distributions for Modeling Location, Scale, and Shape

      DOI link for Distributions for Modeling Location, Scale, and Shape

      Distributions for Modeling Location, Scale, and Shape book

      Using GAMLSS in R

      Distributions for Modeling Location, Scale, and Shape

      DOI link for Distributions for Modeling Location, Scale, and Shape

      Distributions for Modeling Location, Scale, and Shape book

      Using GAMLSS in R
      ByRobert A. Rigby, Mikis D. Stasinopoulos, Gillian Z. Heller, Fernanda De Bastiani
      Edition 1st Edition
      First Published 2019
      eBook Published 7 October 2019
      Pub. Location New York
      Imprint Chapman and Hall/CRC
      DOI https://doi.org/10.1201/9780429298547
      Pages 588
      eBook ISBN 9780429298547
      Subjects Mathematics & Statistics
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      Rigby, R.A., Stasinopoulos, M.D., Heller, G.Z., & De Bastiani, F. (2019). Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9780429298547

      ABSTRACT

      This is a book about statistical distributions, their properties, and their application to modelling the dependence of the location, scale, and shape of the distribution of a response variable on explanatory variables. It will be especially useful to applied statisticians and data scientists in a wide range of application areas, and also to those interested in the theoretical properties of distributions. This book follows the earlier book ‘Flexible Regression and Smoothing: Using GAMLSS in R’, [Stasinopoulos et al., 2017], which focused on the GAMLSS model and software.  GAMLSS (the Generalized Additive Model for Location, Scale, and Shape, [Rigby and Stasinopoulos, 2005]), is a regression framework in which the response variable can have any parametric distribution and all the distribution parameters can be modelled as linear or smooth functions of explanatory variables. The current book focuses on distributions and their application.

      Key features:

      • Describes over 100 distributions, (implemented in the GAMLSS packages in R), including continuous, discrete and mixed distributions.

      • Comprehensive summary tables of the properties of the distributions.

      • Discusses properties of distributions, including skewness, kurtosis, robustness and an important classification of tail heaviness.

      • Includes mixed distributions which are continuous distributions with additional specific values with point probabilities.

      • Includes many real data examples, with R code integrated in the text for ease of understanding and replication.

      • Supplemented by the gamlss website.

      This book will be useful for applied statisticians and data scientists in selecting a distribution for a univariate response variable and modelling its dependence on explanatory variables, and to those interested in the properties of distributions.

      TABLE OF CONTENTS

      part Part I|1 pages

      Parametric distributions and the GAMLSS family of distributions

      chapter 1|18 pages

      Types of distributions

      chapter 2|17 pages

      Properties of distributions

      chapter 3|21 pages

      The GAMLSS family of distributions

      chapter 4|25 pages

      Continuous distributions on (–∞, ∞)

      chapter 5|34 pages

      Continuous distributions on (0, ∞)

      chapter 6|12 pages

      Continuous distributions on (0, 1)

      chapter 7|40 pages

      Discrete count distributions

      chapter 8|10 pages

      Binomial type distributions

      chapter 9|30 pages

      Mixed distributions

      part Part II|2 pages

      Advanced topics

      chapter 10|14 pages

      Statistical inference

      chapter 11|26 pages

      Maximum likelihood estimation

      chapter 12|16 pages

      Robustness of parameter estimation to outlier contamination

      chapter 13|22 pages

      Methods of generating distributions

      chapter 14|12 pages

      Discussion of skewness

      chapter 15|12 pages

      Discussion of kurtosis

      chapter 16|18 pages

      Skewness and kurtosis comparisons of continuous distributions

      chapter 17|36 pages

      Heaviness of tails of distributions

      part Part III|1 pages

      Reference guide

      chapter 18|56 pages

      Continuous distributions on (−∞, ∞)

      chapter 19|34 pages

      Continuous distributions on (0, ∞)

      chapter 20|4 pages

      Mixed distributions on [0, ∞)

      chapter 21|12 pages

      Continuous and mixed distributions on [0,1]

      chapter 22|50 pages

      Discrete count distributions

      chapter 23|9 pages

      Binomial type distributions and multinomial distributions

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