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This is the second part of our book on continuous statistical
distributions. It covers inverse-Gaussian, Birnbaum-Saunders,
Pareto, Laplace, central (2), , , Weibull, Rayleigh, Maxwell, and
extreme value distributions. Important properties of these
distribution are documented, and most common practical applications
are discussed. This book can be used as a reference material for
graduate courses in engineering statistics, mathematical
statistics, and econometrics. Professionals and practitioners
working in various fields will also find some of the chapters to be
useful. Although an extensive literature exists on each of these
distributions, we were forced to limit the size of each chapter and
the number of references given at the end due to the publishing
plan of this book that limits its size. Nevertheless, we gratefully
acknowledge the contribution of all those authors whose names have
been left out. Some knowledge in introductory algebra and college
calculus is assumed throughout the book. Integration is extensively
used in several chapters, and many results discussed in Part I
(Chapters 1 to 9) of our book are used in this volume. Chapter 10
is on Inverse Gaussian distribution and its extensions. The
Birnbaum-Saunders distribution and its extensions along with
applications in actuarial sciences is discussed in Chapter 11.
Chapter 12 discusses Pareto distribution and its extensions. The
Laplace distribution and its applications in navigational errors is
discussed in the next chapter. This is followed by central
chi-squared distribution and its applications in statistical
inference, bioinformatics and genomics. Chapter 15 discusses
Student's distribution, its extensions and applications in
statistical inference. The distribution and its applications in
statistical inference appears next. Chapter 17 is on Weibull
distribution and its applications in geology and reliability
engineering. Next two chapters are on Rayleigh and Maxwell
distributions and its applications in communications, wind energy
modeling, kinetic gas theory, nuclear and thermal engineering, and
physical chemistry. The last chapter is on Gumbel distribution, its
applications in the law of rare exceedances. Suggestions for
improvement are welcome. Please send them to
[email protected].
This is an introductory book on continuous statistical
distributions and its applications. It is primarily written for
graduate students in engineering, undergraduate students in
statistics, econometrics, and researchers in various fields. The
purpose is to give a self-contained introduction to most commonly
used classical continuous distributions in two parts. Important
applications of each distribution in various applied fields are
explored at the end of each chapter. A brief overview of the
chapters is as follows. Chapter 1 discusses important concepts on
continuous distributions like location-and-scale distributions,
truncated, size-biased, and transmuted distributions. A theorem on
finding the mean deviation of continuous distributions, and its
applications are also discussed. Chapter 2 is on continuous uniform
distribution, which is used in generating random numbers from other
distributions. Exponential distribution is discussed in Chapter 3,
and its applications briefly mentioned. Chapter 4 discusses both
Beta-I and Beta-II distributions and their generalizations, as well
as applications in geotechnical engineering, PERT, control charts,
etc. The arcsine distribution and its variants are discussed in
Chapter 5, along with arcsine transforms and Brownian motion. This
is followed by gamma distribution and its applications in civil
engineering, metallurgy, and reliability. Chapter 7 is on cosine
distribution and its applications in signal processing, antenna
design, and robotics path planning. Chapter 8 discusses the normal
distribution and its variants like lognormal, and skew-normal
distributions. The last chapter of Part I is on Cauchy
distribution, its variants and applications in thermodynamics,
interferometer design, and carbon-nanotube strain sensing. A new
volume (Part II) covers inverse Gaussian, Laplace, Pareto, 2, T, F,
Weibull, Rayleigh, Maxwell, and Gumbel distributions.
This is an introductory book on discrete statistical distributions
and its applications. It discusses only those that are widely used
in the applications of probability and statistics in everyday life.
The purpose is to give a self-contained introduction to classical
discrete distributions in statistics. Instead of compiling the
important formulas (which are available in many other textbooks),
we focus on important applications of each distribution in various
applied fields like bioinformatics, genomics, ecology, electronics,
epidemiology, management, reliability, etc., making this book an
indispensable resource for researchers and practitioners in several
scientific fields. Examples are drawn from different fields. An
up-to-date reference appears at the end of the book. Chapter 1
introduces the basic concepts on random variables, and gives a
simple method to find the mean deviation (MD) of discrete
distributions. The Bernoulli and binomial distributions are
discussed in detail in Chapter 2. A short chapter on discrete
uniform distribution appears next. The next two chapters are on
geometric and negative binomial distributions. Chapter 6 discusses
the Poisson distribution in-depth, including applications in
various fields. Chapter 7 is on hypergeometric distribution. As
most textbooks in the market either do not discuss, or contain only
brief description of the negative hypergeometric distribution, we
have included an entire chapter on it. A short chapter on
logarithmic series distribution follows it, in which a theorem to
find the kth moment of logarithmic distribution using (k-1)th
moment of zero-truncated geometric distribution is presented. The
last chapter is on multinomial distribution and its applications.
The primary users of this book are professionals and practitioners
in various fields of engineering and the applied sciences. It will
also be of use to graduate students in statistics, research
scholars in science disciplines, and teachers of statistics,
biostatistics, biotechnology, education, and psychology.
This book introduces descriptive statistics and covers a broad
range of topics of interest to students and researchers in various
applied science disciplines. This includes measures of location,
spread, skewness, and kurtosis; absolute and relative measures; and
classification of spread, skewness, and kurtosis measures, L-moment
based measures, van Zwet ordering of kurtosis, and multivariate
kurtosis. Several novel topics are discussed including the
recursive algorithm for sample variance; simplification of
complicated summation expressions; updating formulas for sample
geometric, harmonic and weighted means; divide-and-conquer
algorithms for sample variance and covariance; L-skewness; spectral
kurtosis, etc. A large number of exercises are included in each
chapter that are drawn from various engineering fields along with
examples that are illustrated using the R programming language.
Basic concepts are introduced before moving on to computational
aspects. Â Some applications in bioinformatics, finance,
metallurgy, pharmacokinetics (PK), solid mechanics, and signal
processing are briefly discussed. Every analyst who works with
numeric data will find the discussion very illuminating and easy to
follow.
STATISTICAL ALGORITHMS integrates up-to-date theoretical and
algorithmic aspects of statistics under one roof. Starting with
elementary algorithms on mean, median and mode, it thoroughly
discusses variance, covariance, correlation, skewness and kurtosis
measures, distance metrics, regression models, and variable
selection methods. The chapter on matrix algorithms summarises a
large number of useful results. Algorithms for the most popular
discrete and continuous statistical distributions appear in
chapters 9 and 10. Estimation in a missing data setup is
numerically exemplified in the chapter on Expectation Maximisation
(EM) algorithm. Random number generation and Monte Carlo methods
are also discussed. A key feature of the book is the large number
of code-snippets and pseudocode of algorithms. No prior knowledge
in statistics or mathematics is assumed on the part of the reader,
but only basic knowledge in computer program coding in any
high-level language. This book is an invaluable resource for
undergraduate students, statisticians and applied mathematicians,
computer scientists, engineers and professionals working in related
fields.
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