Page 10 - Elements of Distribution Theory

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viii Contents

4.5 Moments and Cumulants of the Sample Mean 120
4.6 Conditional Moments and Cumulants 124
4.7 Exercises 127
4.8 Suggestions for Further Reading 130
5. Parametric Families of Distributions 132
5.1 Introduction 132
5.2 Parameters and Identifiability 132
5.3 Exponential Family Models 137
5.4 Hierarchical Models 147
5.5 Regression Models 150
5.6 Models with a Group Structure 152
5.7 Exercises 164
5.8 Suggestions for Further Reading 169
6. Stochastic Processes 170
6.1 Introduction 170
6.2 Discrete-Time Stationary Processes 171
6.3 Moving Average Processes 174
6.4 Markov Processes 182
6.5 Counting Processes 187
6.6 Wiener Processes 192
6.7 Exercises 195
6.8 Suggestions for Further Reading 198

7. Distribution Theory for Functions of Random Variables 199
7.1 Introduction 199
7.2 Functions of a Real-Valued Random Variable 199
7.3 Functions of a Random Vector 202
7.4 Sums of Random Variables 212
7.5 Order Statistics 216
7.6 Ranks 224
7.7 Monte Carlo Methods 228
7.8 Exercises 231
7.9 Suggestions for Further Reading 234
8. Normal Distribution Theory 235
8.1 Introduction 235
8.2 Multivariate Normal Distribution 235
8.3 Conditional Distributions 240
8.4 Quadratic Forms 244
8.5 Sampling Distributions 250
8.6 Exercises 253
8.7 Suggestions for Further Reading 256
9. Approximation of Integrals 257
9.1 Introduction 257
9.2 Some Useful Functions 257
9.3 Asymptotic Expansions 264