Descript 
1 online resource (xxii, 151 pages) 

text txt rdacontent 

computer c rdamedia 

online resource cr rdacarrier 
Series 
Synthesis lectures on mathematics and statistics, 19381751 ; #38


Synthesis lectures on mathematics and statistics ; #38

Note 
Includes bibliographical references (pages 133144) and index 

1. Continuous random variables  1.1. Introduction  1.2. Moments and cumulants  1.3. Sizebiased distributions  1.4. Locationandscale 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 typei beta distribution  4.4. TypeII beta distribution  4.5. Properties of typeii beta distribution  4.6. Sizebiased 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. Skewnormal 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 selfcontained 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 locationandscale distributions, truncated, sizebiased, 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 BetaI and BetaII 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 skewnormal distributions. The last chapter of Part I is on Cauchy distribution, its variants and applications in thermodynamics, interferometer design, and carbonnanotube 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; fulltext 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


sizebiased distributions


survival analysis


truncated distributions


uniform distribution


Electronic books


Electronic books

Alt Author 
Shanmugam, Ramalingam, author

