A primer on statistical distributions

Contents......Page p0004.djvu
Preface......Page p0012.djvu
1.1 Random Variables and Distributions......Page p0014.djvu
1.3 Moment Characteristics......Page p0017.djvu
1.4 Shape Characteristics......Page p0020.djvu
1.5 Entropy......Page p0021.djvu
1.6 Generating Function and Characteristic Function......Page p0023.djvu
1.8 Stable Distributions......Page p0027.djvu
1.9 Random Vectors and Multivariate Distributions......Page p0028.djvu
1.10 Conditional Distributions......Page p0031.djvu
1.11 Moment Characteristics of Random Vectors......Page p0032.djvu
1.12 Conditional Expectations......Page p0033.djvu
1.13 Regressions......Page p0034.djvu
1.14 Generating Function of Random Vectors......Page p0035.djvu
1.15 Transformations of Variables......Page p0037.djvu
I Discrete Distributions......Page p0040.djvu
2.2 Notations......Page p0042.djvu
2.3 Moments......Page p0043.djvu
2.4 Generating Function and Characteristic Function......Page p0046.djvu
2.5 Convolutions......Page p0047.djvu
2.6 Decompositions......Page p0048.djvu
2.8 Relationships with Other Distributions......Page p0049.djvu
3.2 Moments......Page p0052.djvu
3.3 Independence......Page p0053.djvu
3.5 Decomposition......Page p0054.djvu
4.2 Notations......Page p0056.djvu
4.3 Moments......Page p0057.djvu
4.4 Convolutions......Page p0058.djvu
4.5 Maximal Values......Page p0059.djvu
4.6 Relationships with Other Distributions......Page p0060.djvu
5.2 Notations......Page p0062.djvu
5.5 Moments......Page p0063.djvu
5.6 Maximum Probabilities......Page p0066.djvu
5.8 Decompositions......Page p0069.djvu
5.9 Mixtures......Page p0070.djvu
5.10 Conditional Probabilities......Page p0071.djvu
5.12 Limiting Distributions......Page p0072.djvu
6.2 Notations......Page p0076.djvu
6.5 Moments......Page p0077.djvu
6.6 Convolutions......Page p0081.djvu
6.7 Decompositions......Page p0082.djvu
6.8 Entropy......Page p0083.djvu
6.9 Conditional Probabilities......Page p0084.djvu
6.10 Geometric Distribution of Order k......Page p0085.djvu
7.1 Introduction......Page p0086.djvu
7.4 Moments......Page p0087.djvu
7.5 Convolutions and Decompositions......Page p0089.djvu
7.6 Tail Probabilities......Page p0093.djvu
7.7 Limiting Distributions......Page p0094.djvu
8.2 Notations......Page p0096.djvu
8.5 Moments......Page p0097.djvu
8.6 Limiting Distributions......Page p0101.djvu
9.2 Notations......Page p0102.djvu
9.4 Moments......Page p0103.djvu
9.5 Tail Probabilities......Page p0104.djvu
9.7 Decompositions......Page p0105.djvu
9.8 Conditional Probabilities......Page p0107.djvu
9.9 Marginal Probability......Page p0108.djvu
9.11 Mixtures......Page p0109.djvu
9.12 Rao-Rubin Characterization......Page p0112.djvu
9.13 Generalized Poisson Distribution......Page p0113.djvu
10.2 Polya Distribution......Page p0114.djvu
10.3 Pascal Distribution......Page p0115.djvu
10.4 Negative Hypergeometric Distribution......Page p0116.djvu
II Continuous Distributions......Page p0118.djvu
11.2 Notations......Page p0120.djvu
11.3 Moments......Page p0121.djvu
11.6 Convolutions......Page p0123.djvu
11.7 Decompositions......Page p0124.djvu
11.9 Distributions of Minima and Maxima......Page p0125.djvu
11.10 Order Statistics......Page p0127.djvu
11.11 Relationships with Other Distributions......Page p0130.djvu
12.1 Notations......Page p0132.djvu
12.4 Convolutions......Page p0133.djvu
12.7 Transformations......Page p0134.djvu
13.2 Notations......Page p0136.djvu
13.3 Moments......Page p0137.djvu
13.4 Characteristic Function......Page p0138.djvu
14.2 Notations......Page p0140.djvu
14.3 Distributions of Maximal Values......Page p0141.djvu
14.4 Moments......Page p0142.djvu
14.6 Characteristic Function......Page p0144.djvu
15.2 Notations......Page p0146.djvu
15.3 Distributions of Minimal Values......Page p0147.djvu
15.4 Moments......Page p0149.djvu
15.5 Entropy......Page p0150.djvu
16.1 Introduction......Page p0152.djvu
16.3 Mode......Page p0153.djvu
16.5 Moments......Page p0154.djvu
16.7 Characteristic Function......Page p0160.djvu
16.8 Decompositions......Page p0161.djvu
16.9 Relationships with Other Distributions......Page p0162.djvu
17.2 Notations......Page p0164.djvu
17.3 Moments......Page p0166.djvu
17.5 Characteristic Function......Page p0167.djvu
17.7 Characterizations......Page p0168.djvu
17.8 Decompositions......Page p0169.djvu
18.2 Notations......Page p0170.djvu
18.3 Laplace Transform and Characteristic Function......Page p0171.djvu
18.4 Moments......Page p0172.djvu
18.5 Shape Characteristics......Page p0173.djvu
18.7 Distributions of Minima......Page p0175.djvu
18.8 Uniform and Exponential Order Statistics......Page p0176.djvu
18.9 Convolutions......Page p0177.djvu
18.10 Decompositions......Page p0178.djvu
18.11 Lack of Memory Property......Page p0180.djvu
19.2 Notations......Page p0182.djvu
19.3 Characteristic Function......Page p0183.djvu
19.4 Moments......Page p0184.djvu
19.6 Entropy......Page p0185.djvu
19.7 Convolutions......Page p0186.djvu
19.9 Order Statistics......Page p0187.djvu
20.1 Introduction......Page p0192.djvu
20.3 Mode......Page p0193.djvu
20.5 Moments......Page p0194.djvu
20.6 Shape Characteristics......Page p0195.djvu
20.8 Conditional Distributions and Independence......Page p0198.djvu
20.9 Limiting Distributions......Page p0200.djvu
21.1 Introduction......Page p0202.djvu
21.2 Limiting Distributions of Maximal Values......Page p0203.djvu
21.4 Relationships Between Extreme Value Distributions......Page p0204.djvu
21.5 Generalized Extreme Value Distributions......Page p0206.djvu
21.6 Moments......Page p0207.djvu
22.2 Notations......Page p0210.djvu
22.3 Moments......Page p0212.djvu
22.5 Characteristic Function......Page p0214.djvu
22.6 Relationships with Other Distributions......Page p0216.djvu
22.7 Decompositions......Page p0217.djvu
22.9 Generalized Logistic Distributions......Page p0218.djvu
23.1 Introduction......Page p0222.djvu
23.2 Notations......Page p0223.djvu
23.4 Entropy......Page p0224.djvu
23.5 Tail Behavior......Page p0225.djvu
23.6 Characteristic Function......Page p0227.djvu
23.7 Moments......Page p0228.djvu
23.9 Convolutions and Decompositions......Page p0230.djvu
23.10 Conditional Distributions......Page p0232.djvu
23.11 Independence of Linear Combinations......Page p0233.djvu
23.12 Bernstein\'s Theorem......Page p0234.djvu
23.13 Darmois-Skitovitch\'s Theorem......Page p0237.djvu
23.14 Helmert\'s Transformation......Page p0239.djvu
23.15 Identity of Distributions of Linear Combinations......Page p0240.djvu
23.16 Asymptotic Relations......Page p0241.djvu
23.17 Transformations......Page p0242.djvu
24.2 Linnik Distribution......Page p0248.djvu
24.3 Inverse Gaussian Distribution......Page p0250.djvu
24.4 Chi-Square Distribution......Page p0252.djvu
24.5 t Distribution......Page p0253.djvu
24.6 F Distribution......Page p0258.djvu
24.7 Noncentral Distributions......Page p0259.djvu
III Multivariate Distributions......Page p0260.djvu
25.1 Introduction......Page p0262.djvu
25.4 Marginal Distributions......Page p0263.djvu
25.5 Conditional Distributions......Page p0264.djvu
25.6 Moments......Page p0265.djvu
25.7 Generating Function and Characteristic Function......Page p0267.djvu
25.8 Limit Theorems......Page p0269.djvu
26.1 Introduction......Page p0272.djvu
26.2 Notations......Page p0273.djvu
26.5 Linear Combinations of Components......Page p0275.djvu
26.6 Independence of Components......Page p0276.djvu
26.7 Linear Transformations......Page p0277.djvu
26.8 Bivariate Normal Distribution......Page p0278.djvu
27.1 Introduction......Page p0282.djvu
27.2 Derivation of Dirichlet Formula......Page p0284.djvu
27.4 Marginal Distributions......Page p0285.djvu
27.6 Product Moments......Page p0287.djvu
27.7 Dirichlet Distribution of Second Kind......Page p0288.djvu
27.8 Liouville Distribution......Page p0289.djvu
Appendix - Pioneers in Distribution Theory......Page p0290.djvu
Bibliography......Page p0302.djvu
Author Index......Page p0308.djvu
Subject Index......Page p0310.djvu