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Author Chattamvelli, Rajan, author
Title Continuous distributions in engineering and the applied sciences. Part I / Rajan Chattamvelli, Ramalingam Shanmugam
Imprint San Rafael, California (1537 Fourth Street, 1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, [2021]
book jacket
Descript 1 online resource (xxii, 151 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Synthesis lectures on mathematics and statistics, 1938-1751 ; #38
Synthesis lectures on mathematics and statistics ; #38
Note Includes bibliographical references (pages 133-144) and index
1. Continuous random variables -- 1.1. Introduction -- 1.2. Moments and cumulants -- 1.3. Size-biased distributions -- 1.4. Location-and-scale distributions -- 1.5. Truncated distributions -- 1.6. Transmuted distributions -- 1.7. Other extensions -- 1.8. Mean deviation of continuous distributions -- 1.9. Random numbers -- 1.10. Data outliers -- 1.11. Summary
2. Rectangular distribution -- 2.1. Introduction -- 2.2. Related distributions -- 2.3. Properties of rectangular distribution -- 2.4. Applications -- 2.5. Triangular distributions -- 2.6. Summary
3. Exponential distribution -- 3.1. Introduction -- 3.2. Relation to other distributions -- 3.3. Properties of exponential distribution -- 3.4. Random numbers -- 3.5. Fitting -- 3.6. Generalizations -- 3.7. Applications -- 3.8. Summary
4. Beta distribution -- 4.1. Introduction -- 4.2. Relation to other distributions -- 4.3. Properties of type-i beta distribution -- 4.4. Type-II beta distribution -- 4.5. Properties of type-ii beta distribution -- 4.6. Size-biased beta distributions -- 4.7. The incomplete beta function -- 4.8. General beta distribution -- 4.9. Applications -- 4.10. Summary
5. Arcsine distribution -- 5.1. Introduction -- 5.2. Properties of arcsine distribution -- 5.3. Generalized arcsine distributions -- 5.4. Applications -- 5.5. Summary
6. Gamma distribution -- 6.1. Introduction -- 6.2. Alternate representations -- 6.3. Relation to other distributions -- 6.4. Properties of gamma distribution -- 6.5. Tail areas -- 6.6. General gamma distributions -- 6.7. Applications -- 6.8. Summary
7. Cosine distribution -- 7.1. Introduction -- 7.2. Alternate representations -- 7.3. Properties of cosine distribution -- 7.4. Truncated cosine distributions -- 7.5. Special cosine distributions -- 7.6. Applications -- 7.7. Summary
8. Normal distribution -- 8.1. Introduction -- 8.2. Relation to other distributions -- 8.3. Properties of normal distribution -- 8.4. Special normal distributions -- 8.5. Skew-normal distribution -- 8.6. Lognormal distribution -- 8.7. Applications -- 8.8. Summary
9. Cauchy distribution -- 9.1. Introduction -- 9.2. Properties of Cauchy distribution -- 9.3. Relation with other distributions -- 9.4. Special Cauchy distributions -- 9.5. Applications -- 9.6. Summary
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, X2, T, F, Weibull, Rayleigh, Maxwell, and Gumbel distributions
Title from PDF title page (viewed on April 2, 2021)
Abstract freely available; full-text restricted to subscribers or individual document purchasers
Link Print version: 9781636390826 9781636390802
Subject Distribution (Probability theory)
Engineering -- Statistical methods
Science -- Statistical methods
Distribution (Probability theory) fast (OCoLC)fst00895600
Engineering -- Statistical methods. fast (OCoLC)fst00910415
Science -- Statistical methods. fast (OCoLC)fst01108384
actuarial science
antenna design
arcsine distribution
beta distribution
Brownian motion
civil engineering
communication engineering
electronics
exponential distribution
gamma distribution
Gaussian distribution
process control
reliability
robotics
size-biased distributions
survival analysis
truncated distributions
uniform distribution
Electronic books
Electronic books
Alt Author Shanmugam, Ramalingam, author
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