Statistics

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https://en.wikipedia.org/wiki/Template:Statistics
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Monte-Carlo-módszer - Monte Carlo method
Experiment
Data collection
Valószínűség-eloszlások - Probability distribution - Wahrscheinlichkeitsverteilung - Распределение вероятностей
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Statistics
Outline • Index
Descriptive statistics
Continuous data Center Mean • Arithmetic • Cubic • Generalized/power • Geometric • Harmonic • Heinz • Median • Mode
Dispersion Average absolute deviation • Coefficient of variation • Interquartile range • Percentile • Range • Standard deviation • Variance
Shape Central limit theorem • Moments • Kurtosis • L-moments • Skewness
Count data Index of dispersion
Summary tables Contingency table • Frequency distribution • Grouped data
Dependence Partial correlation • Pearson product-moment correlation • Rank correlation • Kendall's τ • Spearman's ρ • Scatter plot
Graphics Bar chart • Biplot • Box plot • Control chart • Correlogram • Fan chart • Forest plot • Histogram • Pie chart • Q-Q plot • Radar chart • Run chart • Scatter plot • Stem-and-leaf display • Violin plot
Data collection
Study design Effect size • Missing data • Optimal design • Population • Replication • Sample size determination • Statistic • Statistical power
Survey methodology Sampling • Cluster • Stratified • Opinion poll • Questionnaire • Standard error
Controlled experiments Blocking • Factorial experiment • Interaction • Random assignment • Randomized controlled trial • Randomized experiment • Scientific control
Adaptive designs Adaptive clinical trial • Stochastic approximation • Up-and-down designs
Observational studies Cohort study • Cross-sectional study • Natural experiment • Quasi-experiment
Statistical inference
Statistical theory Population • Statistic • Probability distribution • Sampling distribution • Order statistic • Empirical distribution • Density estimation • Statistical model • Model specification • Lp space • Parameter • location • scale • shape • Parametric family • Likelihood (monotone) • Location-scale family • Exponential family • Completeness • Sufficiency • Statistical functional • Bootstrap • U • V • Optimal decision • loss function • Efficiency • Statistical distance • divergence • Asymptotics • Robustness
Frequentist inference Point estimation Estimating equations • Maximum likelihood • Method of moments • M-estimator • Minimum distance • Unbiased estimatorsMean-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 • Score/Lagrange multiplier • Wald
Specific tests Z-test (normal) • Student's t-test • F-test
Goodness of fit Chi-squared • G-test • Kolmogorov-Smirnov • Anderson-Darling • Lilliefors • Jarque-Bera • 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) • Van der Waerden test
Bayesian inference Bayesian probability • prior • posterior • Credible interval • Bayes factor • Bayesian estimator • Maximum posterior estimator
Correlation • Regression analysis
Correlation Pearson product-moment • Partial correlation • Confounding variable • Coefficient of determination
Regression analysis Errors and residuals • Regression 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
Categorical / Multivariate / Time-series / Survival analysis
Categorical Cohen's kappa • Contingency table • Graphical model • Log-linear model • McNemar's test • Cochran-Mantel-Haenszel statistics
Multivariate Regression • Manova • Principal components • Canonical correlation • Discriminant analysis • Cluster analysis • Classification • Structural equation model • Factor analysis • Multivariate distributionsElliptical distributions • Normal
Time-series 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 • Least-squares spectral analysis • Wavelet • Whittle likelihood
Survival 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
Applications
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 • Jurimetrics • National accounts • Official statistics • Population statistics • Psychometrics
Spatial statistics Cartography • Environmental statistics • Geographic information system • Geostatistics • Kriging
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