# 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

# 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

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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