Mathematics and statistics

P-curve

P-curve is a meta-analytic technique introduced by Simonsohn, Nelson, and Simmons in 2013 that examines the distribution of significant p-values across studies to detect evidential value or selective reporting, though recent critiques recommend against its use.

P-group

A p-group, also called a primary group, is a group whose every element has order a power of a fixed prime p, central to finite group theory.

p-series

A p-series is an infinite series of the form 1 + 1/2^p + 1/3^p + ... with real exponent p, converging exactly when p > 1 and otherwise diverging.

P-value

The p-value is the probability, assuming the null hypothesis is true, of a result at least as extreme as the observed one; small values are evidence against the null.

PA degree

A PA degree is a Turing degree that computes a complete, consistent extension of Peano Arithmetic; equivalently, one computing a path through every nonempty Pi-0-1 class.

Packing problems

A packing problem asks how to arrange objects in a region without overlap, optimizing density or number of items, from sphere packing to bin packing.

Padé approximant

A Padé approximant is a rational function whose power series expansion matches a given function's series to the highest possible order, often beating truncated Taylor series near poles.

Padovan sequence

The Padovan sequence, also called the Cordonnier sequence, is an integer sequence defined by P(n) = P(n−2) + P(n−3), named by Ian Stewart in 1996.

Painlevé analysis

Painlevé analysis is a singularity-based technique testing whether nonlinear differential equations have only pole-type movable singularities, used to detect integrability and construct exact solutions, Lax pairs, and Bäcklund transformations.

Pairwise comparison

A pairwise comparison is a statistical evaluation of one pair of treatments or items at a time, used to test differences between group means or to rank items from preferences.

Pairwise independence

Pairwise independence is a property in probability theory where every pair of random variables or events is independent, even though the collection as a whole may not be mutually independent.

Palindromic number

A palindromic number, also called a numeral palindrome, reads the same forwards and backwards in some base, such as 121 or 94200249 in decimal.

Pandas (software)

Pandas, also known as Python Pandas, is an open-source Python library for data analysis whose Series and DataFrame structures are built on NumPy; development began in 2008.

Panel cointegration

Panel cointegration methods test whether variables observed for many units over many time periods share long-run equilibrium relationships, and estimate the coefficients of those relationships.

Panel quantile regression

Panel quantile regression estimates conditional quantile effects in longitudinal data while accounting for individual-specific heterogeneity, using penalized fixed effects, two-step, minimum distance, and QRPD estimators.

Panel Study of Income Dynamics

The Panel Study of Income Dynamics (PSID), run by the University of Michigan since 1968, is the longest running longitudinal household survey, tracking US families and their descendants.

Panel threshold model

The panel threshold model is a panel data regression method in which coefficients switch between regimes when a threshold variable crosses an unknown cutoff, introduced by Bruce Hansen in 1999.

Paperwork Reduction Act

The Paperwork Reduction Act is a United States federal law, enacted in 1980, that requires federal agencies to obtain Office of Management and Budget approval before collecting information from the public.

Parabola

A parabola is a plane curve of points equidistant from a fixed focus and a fixed line, the directrix; it is the conic section with eccentricity exactly 1.

Parabolic Anderson model

The parabolic Anderson model is the heat equation with a random potential, modeling electron conduction in defective crystals and known for intermittency, where mass concentrates on rare peaks.

Paraboloid

A paraboloid is a quadric surface with two types, the bowl-shaped elliptic and the saddle-shaped hyperbolic, whose vertical cross sections are parabolas; elliptic paraboloids serve as reflecting antennas and telescopes.

Paracompact space

A paracompact space is a topological space in which every open cover has a locally finite open refinement, a property introduced by Jean Dieudonné in 1944.

Paraconsistent logic

Paraconsistent logic is a family of formal logical systems in which a contradiction does not entail everything: explosion is invalid, so theories containing contradictions can remain non-trivial.

Paradox

A paradox is seemingly sound reasoning from apparently true assumptions that still leads to a contradiction; the Liar dates to antiquity, and Russell's paradox arose in 1901.

Paradoxes of set theory

The paradoxes of set theory are contradictions from naive comprehension, including Russell's paradox (1901), Burali-Forti's (1897), and Cantor's, which forced set theory onto axiomatic foundations.

Parallel (geometry)

In geometry, parallel lines are coplanar straight lines that never meet however far extended, staying a constant distance apart; Euclid's parallel postulate governs them, and denying it yields non-Euclidean geometries.

Parallel analysis

Parallel analysis is a statistical method for deciding how many factors or components to retain in factor analysis, comparing observed eigenvalues against those from random data of the same size.

Parallel and distributed graph algorithms

Parallel and distributed graph algorithms solve graph problems such as connectivity, shortest paths, and matching using many processors or machines, spanning shared-memory, cluster, and network settings.

Parallel factor analysis

Parallel factor analysis (PARAFAC), also called CANDECOMP or CP, is a multi-way decomposition method that models three-way data arrays as sums of trilinear components, widely used in chemometrics.