6,052 articles
Prizes and awards in statistics and probability
Prizes and awards in statistics and probability are honors granted by professional societies such as the ASA, IMS, and RSS, ranging from $2,000 to $1 million.
Probabilistic forecasting
Probabilistic forecasting issues a full probability distribution over future quantities or events instead of a single value, so uncertainty can be quantified and used in decisions.
Probabilistic logic
Probabilistic logic is a family of formal frameworks combining logical representation with probability theory, so inference returns the probability of a query instead of a plain true-or-false verdict.
Probabilistic method
The probabilistic method is a nonconstructive technique for proving a mathematical object exists by showing a randomly chosen object has the property with positive probability, founded by Paul Erdős.
Probabilistic model checking
Probabilistic model checking is an automated verification technique that builds a Markov-chain model of a system and computes probabilities or expectations for properties in probabilistic temporal logic.
Probabilistic number theory
Probabilistic number theory is a branch of number theory treating arithmetic objects as random variables, born with the 1940 Erdős–Kac theorem on prime factors of random integers.
Probabilistic programming languages and systems
A probabilistic programming language (PPL) is a language or embedded library where users write probability models as programs and the system performs inference automatically, pioneered by BUGS in 1994.
Probability
Probability is a numerical measure, between 0 and 1, of how likely an event is, with its mathematical theory tracing to Pascal and Fermat's 1654 correspondence on gambling problems.
Probability axioms
The probability axioms, or Kolmogorov axioms, are three rules defining probability, introduced by Andrey Kolmogorov in 1933 and now the standard foundation of probability theory.
Probability density function
A probability density function (PDF) is a function describing the relative likelihood of values of a continuous random variable, where probabilities are areas under the curve.
Probability distribution
A probability distribution, also known as a probability frequency distribution, is the rule that assigns probabilities to events involving a random variable, such as the chance that X falls between two values.
Probability integral transform
The probability integral transform (PIT) is a result in probability theory: if X has a continuous CDF F, then F(X) follows the uniform distribution on [0, 1].
Probability interpretations
Probability interpretations, also called interpretations of probability, are accounts of what probability statements mean; all share Kolmogorov's 1933 formal calculus but divide over whether probability is physical chance or degree of belief.
Probability mass function
The probability mass function (PMF), also known as the discrete density function, gives the probability that a discrete random variable equals each of its possible values, with all probabilities summing to 1.
Probability measure
A probability measure is a function assigning each event a number between 0 and 1, with total 1 on the whole space, axiomatized by Kolmogorov in 1933.
Probability space
A probability space, or probability triple, is the mathematical object on which probability theory is built: a sample space of outcomes, a collection of events, and a probability measure.
Probability theory
Probability theory is the branch of mathematics that models randomness by assigning numbers between 0 and 1 to events, axiomatized by Andrey Kolmogorov in 1933 using measure theory.
Probability-generating function
A probability-generating function, or PGF, is a power series encoding the probability mass function of a nonnegative integer-valued random variable, used in branching processes and queueing.
Probability-proportional-to-size sampling
Probability-proportional-to-size (PPS) sampling is a survey design in which each unit's selection probability is proportional to a known size measure, standard in two-stage household surveys.
Probit model
The probit model, also called probit analysis or probit regression, is a regression model for binary outcomes using the standard normal CDF, introduced by Chester Bliss in 1934.
Problem of evil
The problem of evil is the philosophical problem of how evil and suffering can coexist with, or count against, an omnipotent, omniscient, and perfectly good God.
Problem of universals
The problem of universals, also called the problem of one and many, asks whether properties, kinds, and relations exist independently of particulars, and how they relate to the things that have them.
Process algebra
Process algebra is a family of formal languages in theoretical computer science that describe concurrent systems as communicating processes, using equational logic to verify their behavior.
Process capability
Process capability is a statistical comparison of an in-control process's output against its specification limits, using dimensionless indices such as Cp, Cpk, and Cpm; a process is capable when nearly all output falls within limits.
Process capability index
The process capability index, or Cpk index, is a statistic comparing a stable process's natural variability with its specification limits; Cp measures spread and Cpk penalizes off-center means.
Procrustes analysis
Procrustes analysis is a statistical method that optimally superimposes one set of points onto another by translation, rotation, reflection, and scaling, yielding the Procrustes distance between shapes.
Product (mathematics)
In mathematics, a product is the result of multiplying numbers or algebraic objects, as in 3 × 4 = 12, and extends to constructions like the Cartesian product.
Product distribution
In probability theory, a product distribution is the distribution of the product of two or more random variables, studied with the Mellin transform and applied in reliability, communications, and finance.
Product measure
A product measure is a measure on the Cartesian product of two measure spaces whose value on a measurable rectangle is the product of the factor measures.
Product rule
The product rule, also called the Leibniz product rule, gives the derivative of a product: (fg)' = f'g + fg'. Leibniz first published it without proof in 1684.