Advanced statistics: distribution theory
This half-course is intended for students who already have some grounding in statistics. It provides the basis for an advanced course in statistical inference.
- Probability measure.
- Conditional probability.
- Bayes’ theorem.
- Distribution function.
- Mass and density.
- Expectation operator.
- Moments, moment generating functions, cumulant generating functions.
- Convergence concepts
- Joint distributions.
- Conditional distributions, conditional moments.
- Functions of random variables.
If you complete the course successfully, you should be able to:
- Recall a large number of distributions and be a competent user of their mass/density and distribution functions and moment generating functions
- Explain relationships between variables, conditioning, independence and correlation
- Relate the theory and method taught in the unit to solve practical problems.
- Grimmett, G. and D. Stirzaker. Probability and Random Processes. OUP. Casella, G. and R.L. Berger. Statistical Inference. Duxbury.