Physical world and mathematics

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 sampling

Probability sampling is a survey sampling method in which every population element has a known, nonzero selection probability, allowing unbiased estimates and measurable sampling error.

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-based online panel

A probability-based online panel is a group recruited by random sampling from a known frame who take repeated surveys, unlike opt-in panels whose members volunteer.

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.

Probable maximum flood

The probable maximum flood (PMF) is the flood resulting from the most severe meteorological and hydrologic conditions reasonably possible for a drainage basin, used as the upper-limit design flood for high-hazard dams.

Probable maximum precipitation

Probable maximum precipitation (PMP) is the greatest rainfall depth meteorologically possible at a location, the design basis for extreme floods at dams and nuclear plants.

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 time

The problem of time is a conceptual obstacle in quantum gravity: time plays fundamentally different roles in general relativity and quantum theory, blocking a single framework.

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.

Proca equation

The Proca equation is the relativistic wave equation for a massive spin-1 particle, proposed by Alexandru Proca in 1936 as a massive generalization of Maxwell's equations.

Procaine benzylpenicillin

Procaine benzylpenicillin, also called procaine penicillin G, is an injectable antibiotic that combines penicillin G with the local anesthetic procaine, released slowly from an intramuscular depot injection.

Procarbazine

Procarbazine, sold in the United States as Matulane, is an oral antineoplastic drug approved by the FDA in 1969 to treat advanced Hodgkin lymphoma in adults and children.

Proceedings of the National Academy of Sciences

Proceedings of the National Academy of Sciences (PNAS) is a multidisciplinary scientific journal published by the US National Academy of Sciences, established in 1914 and first issued in 1915.

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.

Process mass intensity

Process mass intensity (PMI) is a green chemistry metric defined as total raw material mass, including water, divided by the mass of drug product made.

Process tracing

Process tracing is a within-case qualitative method that tests hypotheses about causal mechanisms using diagnostic evidence such as archival documents, interviews, and event sequences, rather than statistical comparison of many cases.

Process zone

A process zone is the region of material damage ahead of a crack tip where nonlinear processes such as plasticity or microcracking locally reduce strength before the crack grows.

Prochirality

Prochirality is the property of an achiral molecule that can become chiral in a single desymmetrization step, such as replacing one of two identical groups.

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.