Distributions

Read these first

1. 01The Lognormal Distribution

   The shape you get when quantities multiply instead of add. It keeps prices positive, pushes the average outcome above the typical one, and is the distribution sitting underneath Black-Scholes.

2. 02The Student's t Distribution

   What the bell curve turns into when you have to estimate the spread from the same small sample you are testing. Fatter tails, wider intervals, and a much better model for daily returns than the normal.

3. 03Extreme Value Theory

   The central limit theorem's counterpart for maxima. It says the worst outcome in a large sample has a predictable shape whatever the underlying data looks like, which is what lets you size a risk limit for a loss you have never actually seen.

4. 04The Exponential Family

   One algebraic template that most named distributions secretly share. Recognise it and you get sufficient statistics, the maximum-likelihood equation, conjugate priors and generalised linear models handed to you for free.

Then the rest

1. 05Maximum Entropy Distributions
2. 06Mixture Distributions
3. 07Quantile Functions and the Inverse CDF
4. 08The Beta Distribution
5. 09The Chi-Squared Distribution
6. 10The Gamma Distribution
7. 11The Pareto Distribution and Power Laws
8. 12The Weibull Distribution
9. 13Truncated and Censored Distributions
10. 14Elliptical Distributions
11. 15Lévy Stable Distributions
12. 16The Cauchy Distribution
13. 17The Generalized Pareto Distribution and Peaks Over Threshold
14. 18The Gumbel Distribution
15. 19The Hill Estimator and Tail Index
16. 20The Wishart Distribution