Resume

Research

Learning

Blog

Teaching

Jokes

Kernel Papers

Many common distributions depend on specific parameters. Parameters are frequently classified into one of several possible types:

- location parameter: shifts the distribution e.g. Gaussian mean
- scale (inverse rate): stretches/squeezes the distribution e.g. Laplace diversity
- shape: changes the shape e.g. Beta \(\alpha, \beta\)

Some common discrete, continuous and special parametric distributions are:

- Bernoulli
- Beta-Bernoulli
- Binomial
- Logarithmic
- Poisson

- Beta
- Cauchy
- Continuous Bernoulli
- Exponential
- Kumaraswamy
- Gamma
- Normal/Gaussian
- von Mises-Fisher

- Elliptical Distributions
- Exponential Family Distributions
- Levy-Stable Distributions
- Location-Scale Distributions

- Probability Space
- Probability Measure
- \(\sigma\)-Algebra
- Random Variables
- Change of variable theorem
- Notions of Convergence

Probability distances and divergences have commonly encountered properties. Some common probability distances and divergences are

- Cramer Distance
- Jensen-Shannon Divergence
- Kullback-Leibler Divergence
- Total Variation Distance
- Wasserstein Distance

**Theorem**: For any random variable \(X\), its CDF \(F_X(x)\)
is distributed uniformly over \((0,1)\). That is, if we define \(Y = F_X(x)\),
then \(Y \sim \mathcal{U}(0,1)\).