\( \newcommand{\E}{\mathbb{E}} \newcommand{\Var}{\operatorname{Var}} \newcommand{\Cov}{\operatorname{Cov}} \newcommand{\Corr}{\operatorname{Corr}} \newcommand{\Prob}{\mathbb{P}} \newcommand{\R}{\mathbb{R}} \newcommand{\N}{\mathbb{N}} \newcommand{\iid}{\overset{\text{i.i.d.}}{\sim}} \newcommand{\dto}{\xrightarrow{d}} \newcommand{\pto}{\xrightarrow{p}} \newcommand{\diff}{\mathop{}\!\mathrm{d}} \)

noisymoon

Notes on distributions, stochastic processes, statistical tests and modeling

Notes on the tools of probability and statistics — definitions, properties and simulations. Formulas are derived from the definitions, and claims are checked with numerical experiments wherever possible. Every method comes with a free in-page demo and a paid HTTP API whose results match R, scipy or statsmodels.

The English edition is growing; more articles are available in Japanese.

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Statistical tests

Derivations of test statistics, null distributions and power.

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