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Probability distribution

Definition

In probability theory and statistics, a probability distribution is a function that gives the probabilities of occurrence of possible events for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events.

Related concepts

(a,b,0) class of distributions ARGUS distribution Absolute continuity Absolutely continuous Absolutely continuous function Absolutely continuous measure Absolutely continuous probability distribution Accelerated failure time model Actuarial science Adaptive clinical trial Akaike information criterion Almost everywhere Almost surely Analysis of covariance Analysis of variance Anderson–Darling test Andrey Kolmogorov Anscombe transform Arcsine distribution Arithmetic mean Arithmetic–geometric mean Asymmetric Laplace distribution Asymptotic theory (statistics)Autocorrelation Autoregressive conditional heteroskedasticity Autoregressive model Autoregressive–moving-average model Average absolute deviation Balding–Nichols model Ball (mathematics)Bar chart Bates distribution Bayes' theorem Bayes estimator Bayes factor Bayesian inference Bayesian information criterion Bayesian linear regression Bayesian probability Benford's law Benini distribution Benktander type II distribution Benktander type I distribution Bernoulli distribution Bernoulli process Bernoulli trial Beta-binomial distribution Beta distribution Beta negative binomial distribution Beta prime distribution Beta rectangular distribution Bias of an estimator Bingham distribution Binomial distribution Binomial regression Bioinformatics Biostatistics Biplot Birgitte Bak-Jensen Bivariate von Mises distribution Blocking (statistics)Boole's inequality Bootstrapping (statistics)Borel distribution Born rule Box plot Box–Cox transformation Box–Jenkins method Breusch–Godfrey test Burr distribution Cache language model Canonical correlation Cantor distribution Cantor set Cartography Categorical distribution Categorical variable Cauchy distribution Census Central limit theorem Central moment Central tendency Characteristic function (probability theory)Chemometrics Chi-squared distribution Chi-squared test Chi distribution Chi squared distribution Christopher Bishop Circular distribution Circular uniform distribution Clinical study design Clinical trial Cluster analysis Cluster sampling Cochran–Mantel–Haenszel statistics Coefficient of determination Coefficient of variation Cohen's kappa Cohort study Coin flipping Cointegration Collectively exhaustive events Combinant Complementary event Completeness (statistics)Complex Wishart distribution Compound Poisson distribution Conditional independence Conditional probability Conditional probability distribution Confidence interval Confounding Conjugate prior Contingency table Continuous Bernoulli distribution Continuous or discrete variable Continuous probability distribution Continuous time Continuous uniform distribution Contraharmonic mean Control chart Convergence of random variables Convex sum Conway–Maxwell–Poisson distribution Correlation and dependence Correlogram Count data Covariance matrix Credible interval Crime statistics Cross-correlation Cross-sectional study Cross-validation (statistics)Cubic mean Cumulant Cumulative distribution function Dagum distribution Daniel W. Stroock Data cleaning Data collection Data preprocessing Data transformation (statistics)Davis distribution Decomposition of time series Degenerate distribution Degrees of freedom (statistics)Delaporte distribution Demographic statistics Density estimation Descriptive statistics Design of experiments Determinism Deterministic system Detrending Dice Dickey–Fuller test Differencing Dimensionality reduction Dirac delta function Dirac measure Directional statistics Dirichlet-multinomial distribution Dirichlet distribution Discrete Weibull distribution Discrete phase-type distribution Discrete probability distribution Discrete uniform distribution Disjoint set Distribution (disambiguation)Divergence (statistics)Durbin–Watson statistic Dynamical systems Econometrics Effect size Efficiency (statistics)Elementary event Elliptical distribution Empirical distribution function Empirical probability Encyclopedia of Mathematics Engineering statistics Environmental statistics Epidemiology Ergodic theory Erhan Çınlar Erlang distribution Errors and residuals Estimating equations European Mathematical Society Event (probability theory)Ewens's sampling formula Expected value Experiment Experiment (probability theory)Exponential-logarithmic distribution Exponential distribution Exponential family Exponential smoothing Extended negative binomial distribution F-distribution F-test Factor analysis Factorial experiment Failure rate Fair coin Fan chart (statistics)Fat-tailed distribution Feature scaling First-hitting-time model Fisher's z-distribution Fisher transformation Flory–Schulz distribution Folded normal distribution Forecasting Forest plot Fourier analysis Fractal Frequency (statistics)Frequency distribution Frequency domain Frequentist inference Friedman test Fréchet distribution Function (mathematics)Fundamental particles G-test Gamma/Gompertz distribution Gamma distribution Gaussian q-distribution Gauss–Kuzmin distribution General linear model Generalised hyperbolic distribution Generalized Dirichlet distribution Generalized Pareto distribution Generalized beta distribution Generalized chi-squared distribution Generalized extreme value distribution Generalized function Generalized gamma distribution Generalized inverse Gaussian distribution Generalized linear model Generalized logistic distribution Generalized mean Generalized normal distribution Geographic information system Geometric distribution Geometric mean Geometric stable distribution Geostatistics Gompertz distribution Goodness of fit Gram Granger causality Graphical model Grouped data Gumbel distribution Half-logistic distribution Half-normal distribution Half-open interval Harmonic mean Hartman–Watson distribution Heatmap Heavy-tailed distribution Heinz mean Heronian mean Histogram Hodges–Lehmann estimator Holtsmark distribution Homoscedasticity and heteroscedasticity Hotelling's T-squared distribution Hyper-Erlang distribution Hyperbolic secant distribution Hypercubes Hyperexponential distribution Hypergeometric distribution Hypoexponential distribution Independence (probability theory)Independent (statistics)Indeterminism Index of dispersion Infinitesimal Integral Integration (mathematics)Interaction (statistics)Interquartile range Interval estimation Inverse-Wishart distribution Inverse-chi-squared distribution Inverse-gamma distribution Inverse Gaussian distribution Inverse matrix gamma distribution Irwin–Hall distribution Isotonic regression Jackknife resampling Jarque–Bera test Jeff Rosenthal Johansen test Johnson's SU-distribution Joint probability distribution Jonckheere's trend test Jump discontinuity Jurimetrics Kaniadakis Erlang distribution Kaniadakis Exponential distribution Kaniadakis Gamma distribution Kaniadakis Gaussian distribution Kaniadakis Logistic distribution Kaniadakis Weibull distribution Kaplan–Meier estimator Kendall rank correlation coefficient Kent distribution Kinetic theory of gases Kolmogorov axioms Kolmogorov–Smirnov test Kriging Kruskal–Wallis test Kumaraswamy distribution Kurtosis L-moment Landau distribution Langmuir waves Laplace distribution Law of large numbers Law of total probability Least-squares spectral analysis Lebesgue's decomposition theorem Lebesgue decomposition theorem Lebesgue measure Lehmann–Scheffé theorem Lehmer mean Lewandowski-Kurowicka-Joe distribution Likelihood-ratio test Likelihood function Likelihood interval Lilliefors test Line chart Linear discriminant analysis Linear regression List of fields of application of statistics List of probability distributions List of statistical tests List of statistical topics List of statistics articles Ljung–Box test Location parameter Location–scale family Log-Cauchy distribution Log-Laplace distribution Log-logistic distribution Log-normal distribution Log-rank test Log-t distribution Log transformation Logarithmic distribution Logistic distribution Logistic regression Logit-normal distribution Lomax distribution Long-tailed distribution Loss function Lp space Lévy distribution M-estimator Mann–Whitney U test Marchenko–Pastur distribution Marginal distribution Markov chain Matrix-exponential distribution Matrix F-distribution Matrix gamma distribution Matrix normal distribution Matrix t-distribution Matrix variate beta distribution Maximum a posteriori estimation Maximum entropy probability distribution Maximum likelihood Maxwell–Boltzmann distribution Maxwell–Jüttner distribution McNemar's test Mean Measurable function Measurable space Measure theory Median Median-unbiased estimator Medical statistics Method of moments (statistics)Methods engineering Minimum-variance unbiased estimator Minimum distance estimation Min–max normalization Missing data Mittag-Leffler distribution Mixed Poisson distribution Mixed model Mixture distribution Mode (statistics)Model selection Model specification Moment (mathematics)Moment generating function Monotone likelihood ratio Monte Carlo method Morris H. DeGroot Multinomial distribution Multiple comparisons Multivariate Laplace distribution Multivariate adaptive regression splines Multivariate analysis of variance Multivariate distribution Multivariate hypergeometric distribution Multivariate normal distribution Multivariate stable distribution Multivariate statistics Multivariate t-distribution Mutual exclusivity Nakagami distribution National accounts Natural experiment Natural exponential family Natural language processing Negative binomial distribution Negative hypergeometric distribution Negative multinomial distribution Nelson–Aalen estimator Non-negative definite Noncentral F-distribution Noncentral beta distribution Noncentral chi-squared distribution Noncentral t-distribution Nonlinear regression Nonparametric regression Nonparametric statistics Normal-Wishart distribution Normal-gamma distribution Normal-inverse-Wishart distribution Normal-inverse-gamma distribution Normal-inverse Gaussian distribution Normal distribution Normalization (statistics)Number Observational study Official statistics One- and two-tailed tests Opinion poll Optimal decision Optimal design Order statistic Ordinary least squares Outcome (probability)Outlier Outline of statistics PERT distribution Parabolic fractal distribution Parametric statistics Pareto distribution Partial autocorrelation function Partial correlation Partition of sums of squares Patrick Billingsley Pearson correlation coefficient Pearson distribution Pearson product-moment correlation coefficient Percentile Permutation test Phase-type distribution Physica Medica Pie chart Pivotal quantity Plasma (physics)Plug-in principle Point estimation Poisson binomial distribution Poisson distribution Poisson regression Poly-Weibull distribution Population (statistics)Population statistics Posterior probability Power-flow study Power (statistics)Power function distribution Power law Power transform Precision (statistics)Prediction Prediction interval Principal component analysis Prior probability Probabilistic design Probability Probability axioms Probability density function Probability distribution fitting Probability generating function Probability mass function Probability measure Probability measures Probability space Probability theory Proportional hazards model Pseudo-random number sampling Pseudorandom number generator Psychometrics Pushforward measure Pólya urn model Q-Gaussian distribution Q-Weibull distribution Q-exponential distribution Quality control Quantile Quantile function Quantum mechanical Quasi-experiment Quasiprobability distribution Questionnaire Q–Q plot R-squared Rabinovich–Fabrikant equations Radar chart Rademacher distribution Raised cosine distribution Random assignment Random matrix Random variable Random variables Random variate Random vector Random walk Randomization test Randomized controlled trial Randomized experiment Randomness Range (statistics)Rank correlation Ranking (statistics)Rao–Blackwell theorem Raw moment Rayleigh distribution Raymond Chang (chemist)Real number Real numbers Realization (probability)Reciprocal distribution Rectified Gaussian distribution Regression analysis Regression validation Relative frequency Relativistic Breit–Wigner distribution Reliability engineering Replication (statistics)Resampling (statistics)Rice distribution Rician fading Riemann–Stieltjes integral Right-continuous Robust regression Robust statistics Run chart Sample (statistics)Sample median Sample size determination Sample space Sample variance Sampling (statistics)Sampling distribution Sampling without replacement Scale parameter Scaled inverse chi-squared distribution Scatter plot Scientific control Score test Seasonal adjustment Semiparametric regression Series (mathematics)Set (mathematics)Shape of the distribution Shape parameter Shapiro–Wilk test Sheldon M. Ross Shifted Gompertz distribution Shifted log-logistic distribution Sign test Simple linear regression Simultaneous equations model Singleton (mathematics)Singular distribution Skellam distribution Skew normal distribution Skewness Slash distribution Social statistics Soliton distribution Spatial analysis Spearman's rank correlation coefficient Spectral density estimation Stable distribution Standard deviation Standard error Standard normal Standard score Standardized moment Stationary process Statistic Statistical Language Model Statistical classification Statistical dispersion Statistical distance Statistical graphics Statistical hypothesis test Statistical inference Statistical model Statistical parameter Statistical population Statistical power Statistical process control Statistical theory Statistics Stem-and-leaf display Stochastic approximation Stochastic process Stochastic processes Stratified sampling Structural break Structural equation modeling Student's t-distribution Student's t-test Student's t distribution Subset Sufficient statistic Support (measure theory)Survey methodology Survival analysis Survival function Symmetric probability distribution System identification System of differential equations Time domain Time series Tolerance interval Tracy–Widom distribution Tree diagram (probability theory)Trend estimation Triangular distribution Triple integral Tropical cyclone Truncated normal distribution Truncation (statistics)Tukey lambda distribution Tweedie distribution Type-2 Gumbel distribution U-quadratic distribution U-statistic Uniform distribution (continuous)Uniform distribution (discrete)Uniform distribution on a Stiefel manifold Uniformly most powerful test Unit vector normalization Univariate distribution Up-and-Down Designs V-statistic Van der Waerden test Variance Variance-gamma distribution Variance-stabilizing transformation Vector (mathematics)Vector autoregression Vector space Venn diagram Violin plot Voigt profile Von Mises distribution Von Mises–Fisher distribution Wald test Wavefunction Wavelet Weibull distribution Weighted average Whittle likelihood Wigner semicircle distribution Wilcoxon signed-rank test Wilks's lambda distribution Winsorizing Wishart distribution Wrapped Cauchy distribution Wrapped Lévy distribution Wrapped asymmetric Laplace distribution Wrapped distribution Wrapped exponential distribution Wrapped normal distribution Yeo–Johnson transformation Yule–Simon distribution Z-test Zeta distribution Zipf's law Zipf–Mandelbrot law Σ-algebra

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