Title Discrete distributions in engineering and the applied sciences / Rajan Chattamvelli and Ramalingam Shanmugam

Published Cham, Switzerland : Springer, [2020] ©2020

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Description 1 online resource (xxi, 205 pages) : illustrations Series Synthesis lectures on mathematics and statistics ; #34 Synthesis lectures on mathematics and statistics ; #34. Contents 1. Discrete random variables -- 1.1. Introduction -- 1.2. Discrete random variables -- 1.3. Conditional models -- 1.4. Linear combination of random variables -- 1.5. Domain of a random variable -- 1.6. Cdf and sf -- 1.7. Binomial theorem -- 1.8. Mean deviation of discrete distributions -- 1.9. Truncated models -- 1.10. Zero-inflated distributions -- 1.11. Hurdle models -- 1.12. Power series distributions -- 1.13. Summary 2. Binomial distribution -- 2.1. Introduction -- 2.2. Bernoulli distribution -- 2.3. Binomial distribution -- 2.4. Properties of binomial distribution -- 2.5. Generating functions -- 2.6. Algorithm for computing binomial distribution -- 2.7. Limiting form of binomial distribution -- 2.8. Special binomial distributions -- 2.9. Applications -- 2.10. Summary 3. Discrete uniform distribution -- 3.1. Introduction -- 3.2. Discrete uniform distribution -- 3.3. Properties of discrete uniform distribution -- 3.4. Relation to other distributions -- 3.5. Applications -- 3.6. Summary 4. Geometric distribution -- 4.1. Derivation -- 4.2. Relation to other distributions -- 4.3. Properties of geometric distribution -- 4.4. Special geometric distributions -- 4.5. Random samples -- 4.6. Applications -- 4.7. Summary 5. Negative binomial distribution -- 5.1. Derivation -- 5.2. Relation to other distributions -- 5.3. Properties of NBINO(k,p) -- 5.4. Poisson approximation -- 5.5. Moment recurrence -- 5.6. Tail probabilities -- 5.7. Truncated negative binomial distributions -- 5.8. Generalizations -- 5.9. Applications -- 5.10. Summary 6. Poisson distribution -- 6.1. Introduction -- 6.2. Probability mass function -- 6.3. Dilution techniques -- 6.4. Moment approximation -- 6.5. Derivation of Poisson law -- 6.6. Properties of Poisson distribution -- 6.7. Relation to other distributions -- 6.8. Algorithms for Poisson distribution -- 6.9. Approximations -- 6.10. Generalized Poisson distributions -- 6.11. Poisson process -- 6.12. Fitting a Poisson distribution -- 6.13. Truncated Poisson distribution -- 6.14. Zero-inflated Poisson distribution -- 6.15. Double poissOn distribution -- 6.16. Applications -- 6.17. Summary 7. Hypergeometric distribution -- 7.1. Introduction -- 7.2. Alternate forms -- 7.3. Relation to other distributions -- 7.4. Properties of hypergeometric distribution -- 7.5. Truncated hypergeometric distributions -- 7.6. Applications -- 7.7. Summary 8. Negative hypergeometric distribution -- 8.1. Derivation -- 8.2. Alternate forms -- 8.3. Properties of NHGD -- 8.4. Truncated NHGD -- 8.5. Applications -- 8.6. Summary 9. Logarithmic series distribution -- 9.1. Introduction -- 9.2. Properties of logarithmic distribution -- 9.3. Zero-inflated logarithmic distribution -- 9.4. Lagrangian logarithmic distribution -- 9.5. Applications -- 9.6. Summary 10. Multinomial distribution -- 10.1. Introduction -- 10.2. Relation to other distributions -- 10.3. Properties of multinomial distribution. -- 10.4. Applications -- 10.5. Summary Summary 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 kthth 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 Analysis additivity algorithms biostatistics biotechnology capture-recapture model combinatorics electronics generating functions highway engineering mean deviation negative hypergeometric distribution Poisson limit theorem probability distributions quality control random variables special functions Stirling distributions Stirling numbers survival function truncated distribution variance generating function zero-inflated distributions Bibliography Includes bibliographical references (pages 189-197) and index Subject Engineering -- Statistical methods. Mathematical statistics. Poisson distribution. Poisson Distribution Engineering -- Statistical methods Mathematical statistics Poisson distribution Form Electronic book Author Shanmugam, Ramalingam, author. ISBN 9781681738642 1681738643 9783031024252 3031024257

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