Probability and statistics

Probability

Outline Catalog of articles Probabilists Glossary Notation Journals Category

Probability and Statistics or also called Statistics and Probability are two related but separate academic disciplines. Statistical analysis often uses probability distributions, and the two topics are often studied together. However, probability theory contains much that is mostly of mathematical interest and not directly relevant to statistics. Moreover, many topics in statistics are independent of probability theory.

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Center	Mean arithmetic geometric harmonic Median Mode

Dispersion	Variance Standard deviation Coefficient of variation Percentile Range Interquartile range

Shape	Moments Skewness Kurtosis L-moments

Summary tables

Study design	Population Statistic Effect size Statistical power Sample size determination Missing data

Survey methodology	Sampling Standard error stratified cluster Opinion poll Questionnaire

Controlled experiments	Design control optimal Controlled trial Randomized Random assignment Replication Blocking Interaction Factorial experiment

Uncontrolled studies	Observational study Natural experiment Quasi-experiment

Point estimation	Estimating equations Maximum likelihood Method of moments M-estimator Minimum distance Unbiased estimators Mean-unbiased minimum-variance Rao–Blackwellization Lehmann–Scheffé theorem Median unbiased Plug-in

Interval estimation	Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife

Testing hypotheses	1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons

Parametric tests	Likelihood-ratio Wald Score

Specific tests

Z (normal) Student's t-test F

Goodness of fit	Chi-squared Kolmogorov–Smirnov Anderson–Darling Normality (Shapiro–Wilk) Likelihood-ratio test Model selection Cross validation AIC BIC

Rank statistics	Sign Sample median Signed rank (Wilcoxon) Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra)

Correlation	Pearson product–moment Partial correlation Confounding variable Coefficient of determination

Regression analysis	Errors and residuals Regression model validation Mixed effects models Simultaneous equations models Multivariate adaptive regression splines (MARS)

Linear regression	Simple linear regression Ordinary least squares General linear model Bayesian regression

Non-standard predictors	Nonlinear regression Nonparametric Semiparametric Isotonic Robust Heteroscedasticity Homoscedasticity

Generalized linear model	Exponential families Logistic (Bernoulli) / Binomial / Poisson regressions

Partition of variance	Analysis of variance (ANOVA, anova) Analysis of covariance Multivariate ANOVA Degrees of freedom

General	Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration Structural break Granger causality

Specific tests	Dickey–Fuller Johansen Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey

Time domain	Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional heteroskedasticity (ARCH) Vector autoregression (VAR)

Frequency domain	Spectral density estimation Fourier analysis Wavelet

Survival function	Kaplan–Meier estimator (product limit) Proportional hazards models Accelerated failure time (AFT) model First hitting time

Hazard function	Nelson–Aalen estimator

Test	Log-rank test

Biostatistics	Bioinformatics Clinical trials / studies Epidemiology Medical statistics

Engineering statistics	Chemometrics Methods engineering Probabilistic design Process / quality control Reliability System identification

Social statistics	Actuarial science Census Crime statistics Demography Econometrics National accounts Official statistics Population statistics Psychometrics

Spatial statistics	Cartography Environmental statistics Geographic information system Geostatistics Kriging

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