273 articles
Categorical distribution
The categorical distribution, also called the multinoulli distribution, is the discrete probability distribution of a single draw landing in one of k categories, each with a specified probability.
Cauchy distribution
The Cauchy distribution, also known as the Lorentz distribution, is a continuous probability distribution that resembles the normal distribution but has heavier tails, so its mean and variance do not exist.
Central limit theorem
The central limit theorem (CLT) is a probability theorem stating that standardized sums of many independent random variables converge to a normal distribution regardless of their shape, underpinning parametric statistics.
Central moment
A central moment, or moment about the mean, of a random variable measures the distribution's shape about its own center; the variance, skewness, and kurtosis are scaled central moments.
Change of variables for random variables
The change of variables for random variables is a formula giving the density of Y = g(X) from the density of X, using the Jacobian of the inverse transformation.
Characteristic function (probability theory)
In probability theory, the characteristic function of a random variable is the Fourier transform φ(t) = E[e^{itX}], which always exists and uniquely determines the distribution.
Chebyshev's inequality
Chebyshev's inequality, also called the Bienaymé-Chebyshev inequality, is a theorem of probability theory stating that a random variable lies more than ε from its mean with probability at most Var(X)/ε².
Chernoff bound
The Chernoff bound, also known as Chernoff's inequality, is an exponential upper bound on tail probabilities of random variables, especially sums of independent variables, developed by Herman Chernoff in 1952.
Chi-squared distribution
The chi-squared (χ²) distribution is a continuous probability distribution arising from the sum of squares of standard normal variables, widely used in statistics for goodness-of-fit and independence tests.
Coherent risk measure
A coherent risk measure assigns a capital-like number to a financial position while satisfying four axioms, including subadditivity, so diversification is never penalized; introduced by Artzner, Delbaen, Eber, and Heath in 1999.
Coin flipping
Coin flipping, also called coin tossing or heads or tails, is throwing a coin to choose between two alternatives, treated as a random event with even odds.
Collectively exhaustive events
Collectively exhaustive events, also called jointly exhaustive events, are events in probability theory that together cover the entire sample space, so at least one must occur.
Comonotonicity
Comonotonicity is an extremal form of positive dependence among random variables, where each is a non-decreasing function of a common factor, central to actuarial science and financial mathematics.
Complex normal distribution
The complex normal distribution, also called the complex Gaussian distribution, describes complex-valued random variables and vectors whose real and imaginary parts are jointly Gaussian, with a mean and covariance.
Complex random variable
A complex random variable is a complex-valued function on a probability space, equivalent to a pair of real random variables, used to model signals in communication and signal processing.
Complex random vector
A complex random vector is a jointly distributed collection of complex-valued random variables, used to model baseband noise and signals in digital communications, radar, and array processing.
Compound probability distribution
A compound probability distribution, also called a compound distribution, is the distribution of a sum of a random number of random variables, used to model insurance claims.
Concentration inequality
A concentration inequality is a mathematical bound on how likely a function of many random variables, like a sum, is to deviate far from its expected value.
Concentration of measure
Concentration of measure is a phenomenon of high-dimensional probability in which a function of many random variables takes values in a narrow range with overwhelming probability.
Conditional entropy
Conditional entropy, written H(Y|X), measures in information theory the average uncertainty remaining in a random variable Y once another variable X is known; Claude Shannon introduced it in 1948.
Conditional expectation
Conditional expectation, also known as conditional mean, is the expected value of a random variable once part of the outcome is known, defined via sub-σ-algebras by Kolmogorov in 1933.
Conditional independence
Conditional independence is the property that two quantities carry no information about each other once a third quantity is known; it underlies graphical models and sufficiency theory.
Conditional probability
Conditional probability is the probability of an event given that another has occurred, defined as P(A∩B)/P(B) for P(B) > 0; it underlies Bayes' rule and conditioning in statistics.
Conditional probability distribution
A conditional probability distribution is the distribution of a random variable given other information, such as Y = y, computed as a joint distribution divided by a marginal.
Conditional variance
Conditional variance, also called the scedastic or skedastic function, is the variance of a random variable once another variable is known, and it obeys the law of total variance.
Configuration model (network science)
The configuration model is a random graph model in network science that generates networks with a prescribed degree sequence, built by pairing stubs uniformly at random.
Conjunction fallacy
The conjunction fallacy, or conjunction effect, is a reasoning error in which a combination of two events is judged more probable than one event alone.
Continuous mapping theorem
The continuous mapping theorem, or Mann–Wald theorem, states that convergence of random variables is preserved under continuous functions, and underlies Slutsky's theorem and the delta method.
Continuous or discrete variable
In probability and statistics, a discrete variable takes countable values such as die rolls, while a continuous variable takes any value in an interval, like height or temperature.
Continuous uniform distribution
The continuous uniform distribution, also called the rectangular distribution, gives every value in a fixed interval equal probability, with constant density across the interval and zero outside it.