Chapter 15. The Gamma Function and Related Distributions

Chapters in this book

1. Frontmatter i
2. Contents v
3. Note to Readers xv
4. How to Use this Book xix
5. Part I. General Theory
6. Chapter 1. Introduction 3
7. Chapter 2. Basic Probability Laws 40
8. Chapter 3. Counting I: Cards 78
9. Chapter 4. Conditional Probability, Independence, and Bayes′ Theorem 128
10. Chapter 5. Counting II: Inclusion-Exclusion 156
11. Chapter 6. Counting III: Advanced Combinatorics 186
12. Part II. Introduction to Random Variables
13. Chapter 7. Introduction to Discrete Random Variables 221
14. Chapter 8. Introduction to Continuous Random Variables 238
15. Chapter 9. Tools: Expectation 254
16. Chapter 10. Tools: Convolutions and Changing Variables 285
17. Chapter 11. Tools: Differentiating Identities 309
18. Part III. Special Distributions
19. Chapter 12. Discrete Distributions 327
20. Chapter 13. Continuous Random Variables: Uniform and Exponential 349
21. Chapter 14. Continuous Random Variables: The Normal Distribution 371
22. Chapter 15. The Gamma Function and Related Distributions 398
23. Chapter 16. The Chi-square Distribution 427
24. Part IV. Limit Theorems
25. Chapter 17. Inequalities and Laws of Large Numbers 449
26. Chapter 18. Stirling’s Formula 469
27. Chapter 19. Generating Functions and Convolutions 494
28. Chapter 20. Proof of the Central Limit Theorem 527
29. Chapter 21. Fourier Analysis and the Central Limit Theorem 553
30. Part V. Additional Topics
31. Chapter 22. Hypothesis Testing 569
32. Chapter 23. Difference Equations, Markov Processes, and Probability 607
33. Chapter 24. The Method of Least Squares 625
34. Chapter 25. Two Famous Problems and Some Coding 636
35. Appendix A. Proof Techniques 649
36. Appendix B. Analysis Results 675
37. Appendix C. Countable and Uncountable Sets 693
38. Appendix D. Complex Analysis and the Central Limit Theorem 704
39. Bibliography 717
40. Index 721