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A probability measure on a measurable value space, including the pushforward law of a random variable.
A distribution need not possess a density; discrete, continuous, singular, and mixed probability laws are all included.
wp-probability-distributionnlab-probability-distributiondurrett-probabilityEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The law of is the pushforward measure on its measurable value space.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-probability-distributionnlab-probability-distributiondurrett-probabilityEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A real probability distribution with finite absolute first moment determines its mean by integrating the identity function.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-expected-valuewp-probability-distributiondurrett-probabilityThis is an authored directed relation from the source endpoint to the target endpoint.
Under an explicit measurement model, a probability distribution can represent knowledge about a chemical measurand; this does not identify uncertainty with repeatability, instrument resolution, or a population frequency.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-probability-distributionnlab-probability-distributionwp-chem-analytical-chemistryiupac-orange-bookThis is an authored directed relation from the source endpoint to the target endpoint.
Normal distributions form the Gaussian location-scale subclass of probability distributions on the real line.
The target is a member or subtype of the broader source class.
wp-normal-distributionnlab-gaussian-distributiondurrett-probabilityThis is an authored directed relation from the source endpoint to the target endpoint.
A classical statistical ensemble is formulated as a probability measure on a specified microstate space. Quantum ensembles instead use density operators, so the probability-distribution formulation is not the whole target concept.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-probability-distributionwp-physics-statistical-ensembletong-statistical-physics