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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.
This book is about learning from data using the Generalized
Additive Models for Location, Scale and Shape (GAMLSS). GAMLSS
extends the Generalized Linear Models (GLMs) and Generalized
Additive Models (GAMs) to accommodate large complex datasets, which
are increasingly prevalent. In particular, the GAMLSS statistical
framework enables flexible regression and smoothing models to be
fitted to the data. The GAMLSS model assumes that the response
variable has any parametric (continuous, discrete or mixed)
distribution which might be heavy- or light-tailed, and positively
or negatively skewed. In addition, all the parameters of the
distribution (location, scale, shape) can be modelled as linear or
smooth functions of explanatory variables. Key Features: Provides a
broad overview of flexible regression and smoothing techniques to
learn from data whilst also focusing on the practical application
of methodology using GAMLSS software in R. Includes a comprehensive
collection of real data examples, which reflect the range of
problems addressed by GAMLSS models and provide a practical
illustration of the process of using flexible GAMLSS models for
statistical learning. R code integrated into the text for ease of
understanding and replication. Supplemented by a website with code,
data and extra materials. This book aims to help readers understand
how to learn from data encountered in many fields. It will be
useful for practitioners and researchers who wish to understand and
use the GAMLSS models to learn from data and also for students who
wish to learn GAMLSS through practical examples.
This book is about learning from data using the Generalized
Additive Models for Location, Scale and Shape (GAMLSS). GAMLSS
extends the Generalized Linear Models (GLMs) and Generalized
Additive Models (GAMs) to accommodate large complex datasets, which
are increasingly prevalent. In particular, the GAMLSS statistical
framework enables flexible regression and smoothing models to be
fitted to the data. The GAMLSS model assumes that the response
variable has any parametric (continuous, discrete or mixed)
distribution which might be heavy- or light-tailed, and positively
or negatively skewed. In addition, all the parameters of the
distribution (location, scale, shape) can be modelled as linear or
smooth functions of explanatory variables. Key Features: Provides a
broad overview of flexible regression and smoothing techniques to
learn from data whilst also focusing on the practical application
of methodology using GAMLSS software in R. Includes a comprehensive
collection of real data examples, which reflect the range of
problems addressed by GAMLSS models and provide a practical
illustration of the process of using flexible GAMLSS models for
statistical learning. R code integrated into the text for ease of
understanding and replication. Supplemented by a website with code,
data and extra materials. This book aims to help readers understand
how to learn from data encountered in many fields. It will be
useful for practitioners and researchers who wish to understand and
use the GAMLSS models to learn from data and also for students who
wish to learn GAMLSS through practical examples.
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.
This is the only book actuaries need to understand generalized
linear models (GLMs) for insurance applications. GLMs are used in
the insurance industry to support critical decisions. Until now, no
text has introduced GLMs in this context or addressed the problems
specific to insurance data. Using insurance data sets, this
practical, rigorous book treats GLMs, covers all standard
exponential family distributions, extends the methodology to
correlated data structures, and discusses recent developments which
go beyond the GLM. The issues in the book are specific to insurance
data, such as model selection in the presence of large data sets
and the handling of varying exposure times. Exercises and
data-based practicals help readers to consolidate their skills,
with solutions and data sets given on the companion website.
Although the book is package-independent, SAS code and output
examples feature in an appendix and on the website. In addition, R
code and output for all the examples are provided on the website.
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