Probability

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12 domain-specific abstractions whose origin domain is Probability.

• Brownian snake — A Markov process taking values in finite stopped paths whose lifetime evolves like reflected Brownian motion and whose path tips encode spatial genealogies such as superprocesses.
• Continuous Uniform Distribution — The bounded continuous probability law whose density is constant, assigning probability in direct proportion to interval length.
• Displaced Poisson Distribution — A Poisson-tail count law obtained by conditioning on at least an integer threshold and counting the excess, equivalently shifting the Poisson probability recurrence.
• Doob martingale — Track the evolving conditional expectation E[Y|F_t] of an integrable target as a filtration reveals information, producing a martingale of progressively refined best predictions.
• Generalized chi-squared distribution — The probability distribution of a quadratic function of a multivariate normal vector, equivalently a weighted sum of independent noncentral chi-square variables with an optional normal term.
• K-Distribution — A compound positive-valued distribution obtained by mixing fast speckle with a gamma-distributed local mean, producing a Bessel-K density with convention-dependent tail behavior.
• Law of total probability — A probability identity expressing an event's probability as the sum or integral of its conditional probabilities over a mutually exclusive exhaustive partition.
• Matrix Chernoff Bound — A spectral concentration inequality controlling extreme eigenvalues of sums of independent bounded positive-semidefinite random matrices.
• Multivariate Pareto distribution — A family of joint heavy-tailed distributions whose margins have Pareto-type behavior and whose dependence construction models simultaneous extremes across variables.
• Poisson boundary — A measure-theoretic boundary of a random walk that captures its asymptotic tail behavior and represents bounded harmonic functions by boundary data.
• Q-function — Map a real threshold to the upper-tail probability of a standard normal variable, equivalently one half of the complementary error function at the threshold divided by the square root of two.
• Tail dependence — Measure whether two continuously distributed variables continue to co-exceed matched extreme quantiles by taking an upper- or lower-tail conditional-probability limit determined by their copula rather than their marginal scales.