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Statistics concept
In statistics, a generalized p-value is an extended version of the classical p-value, which except in a limited number of applications, provides only
Generalized_p-value
Function of the observed sample results
method of combining p-values Generalized p-value Harmonic mean p-value Holm–Bonferroni method Multiple comparisons problem p-rep p-value fallacy Italicisation
P-value
Family of probability distributions
statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value theory to combine
Generalized extreme value distribution
Generalized_extreme_value_distribution
Name of two different techniques based on the singular value decomposition
linear algebra, the generalized singular value decomposition (GSVD) is the name of two different techniques based on the singular value decomposition (SVD)
Generalized singular value decomposition
Generalized_singular_value_decomposition
Class of statistical models
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing
Generalized_linear_model
Type of statistic
variances. To rectify this situation, the generalized p-values are defined as an extension of the classical p-values so that one can perform tests based on
Exact_statistics
Commonly known as generalized inferences, the new concepts include generalized p-value generalized confidence intervals and generalized point estimation
Sam_Weerahandi
Family of probability distributions often used to model tails or extreme values
In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions. It is often used to model the tails of another
Generalized Pareto distribution
Generalized_Pareto_distribution
Statistical concept
reciprocal of an e-value is a p-value, but not just any p-value: a special p-value for which a rejection `at level p' retains a generalized Type-I error guarantee
E-values
Statistics models class
In statistics, a generalized additive model (GAM) is a generalized linear model in which the linear response variable depends linearly on unknown smooth
Generalized_additive_model
Objects extending the notion of functions
theory of generalized functions in order to define weak solutions of partial differential equations (i.e. solutions which are generalized functions,
Generalized_function
mathematics, a p-adic distribution is an analogue of ordinary distributions (i.e. generalized functions) that takes values in a ring of p-adic numbers.
P-adic_distribution
distribution Generalized normal distribution Generalized p-value Generalized Pareto distribution Generalized Procrustes analysis Generalized randomized
List_of_statistics_articles
Positive integer of the form (2^(2^n))+1
primes today are generalized Fermat primes. Generalized Fermat numbers can be prime only for even a, because if a is odd then every generalized Fermat number
Fermat_number
N-th root of the arithmetic mean of the given numbers raised to the power n
inequality for negative p and q by replacing them with −q and −p, respectively. The power mean could be generalized further to the generalized f-mean: M f ( x
Generalized_mean
Search auction mechanism
The generalized second-price auction (GSP) is a non-truthful auction mechanism for multiple items. Each bidder places a bid. The highest bidder gets the
Generalized second-price auction
Generalized_second-price_auction
Number system extending the rational numbers
such as 1 p {\displaystyle {\tfrac {1}{p}}} , cannot be written as a p-adic integer. Because of this, p-adic integers are generalized further to p-adic numbers:
P-adic_number
Multivariate derivative (mathematics)
vector-valued function) ∇ f {\displaystyle \nabla f} whose value at a point p {\displaystyle p} gives the direction and the rate of fastest increase. The
Gradient
Method for estimating the unknown parameters in a linear regression model
the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the
Ordinary_least_squares
Probability distribution
The generalized normal distribution (GND) or generalized Gaussian distribution (GGD) is either of two parametric families of continuous probability distributions
Generalized normal distribution
Generalized_normal_distribution
System configuration relative to another
configuration. The generalized velocities are the time derivatives of the generalized coordinates of the system. The adjective "generalized" distinguishes
Generalized_coordinates
Instantaneous rate of change (mathematics)
velocity, and the second derivative is its acceleration. Derivatives can be generalized to functions of several real variables. In this case, the derivative
Derivative
Nonspecific long-lasting anxiety
Generalized anxiety disorder (GAD) is an anxiety disorder characterized by excessive, uncontrollable, and often irrational worry about events or activities
Generalized_anxiety_disorder
Number taken as representative of a list of numbers
minimizing variation can be generalized in information geometry as a distribution that minimizes divergence (a generalized distance) from a data set. The
Average
Point to which functions converge in analysis
limit L at an input p, if f(x) gets closer and closer to L as x moves closer and closer to p. More specifically, the output value can be made arbitrarily
Limit_of_a_function
Computational quantum mechanical modelling method to investigate electronic structure
states in the absence of a magnetic field, although they have since been generalized to encompass these. The first HK theorem demonstrates that the ground-state
Density_functional_theory
Most widely known generalized inverse of a matrix
= A + {\textstyle A^{+}AA^{+}=A^{+}} , it is called a generalized reflexive inverse. Generalized inverses always exist but are not in general unique. Uniqueness
Moore–Penrose_inverse
Injective polynomial functions are bijective
{\displaystyle P} is bijective. That is, if P {\displaystyle P} always maps distinct arguments to distinct values, then the values of P {\displaystyle P} cover
Ax–Grothendieck_theorem
Particular case of the generalized extreme value distribution
statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum
Gumbel_distribution
Vector satisfying some of the criteria of an eigenvector
linearly independent generalized eigenvectors which form a basis for an invariant subspace of V {\displaystyle V} . Using generalized eigenvectors, a set
Generalized_eigenvector
In mathematical analysis, the mean value theorem for divided differences generalizes the mean value theorem to higher derivatives. For any n + 1 pairwise
Mean value theorem (divided differences)
Mean_value_theorem_(divided_differences)
Auction priced by second-highest sealed bid
but uncommon in practice. Generalized variants of the Vickrey auction for multiunit auctions exist, such as the generalized second-price auction used
Vickrey_auction
Anxiety disorder screening instrument
The Generalized Anxiety Disorder 7-item scale (GAD-7) is a widely used self-administered diagnostic tool designed to screen for and assess the severity
Generalized Anxiety Disorder 7
Generalized_Anxiety_Disorder_7
Algebraic element satisfying some of the criteria of an inverse
}A=A.} A generalized inverse exists for an arbitrary matrix, and when a matrix has a regular inverse, this inverse is its unique generalized inverse.
Generalized_inverse
Differential operator in mathematics
Laplacian Δf (p) of a function f at a point p measures by how much the average value of f over small spheres or balls centered at p deviates from f (p). The Laplace
Laplace_operator
Matrix with one nonzero entry in each row and column
nonzero entry must be 1, in a generalized permutation matrix the nonzero entry can be any nonzero value. An example of a generalized permutation matrix is [
Generalized permutation matrix
Generalized_permutation_matrix
Branch of statistics focusing on large deviations
results of the Fisher–Tippett–Gnedenko theorem, leading to the generalized extreme value distribution being selected for fitting. However, in practice
Extreme_value_theory
Expresses a Gauss sum using a product of values of the p-adic gamma function
Gross and Koblitz (1979) expresses a Gauss sum using a product of values of the p-adic gamma function. It is an analog of the Chowla–Selberg formula
Gross–Koblitz_formula
Matrix of partial derivatives of a vector-valued function
vector-valued function in several variables generalizes the gradient of a scalar-valued function in several variables, which in turn generalizes the derivative
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Measure used in functional analysis
needed] They are generalized by positive operator valued measures (POVMs) in the same sense that a mixed state or density matrix generalizes the notion of
Projection-valued_measure
Conjecture about prime gaps
to 246. Further, assuming the Elliott–Halberstam conjecture and its generalized form, the Polymath project wiki states that n has been reduced to 12
Polignac's_conjecture
takes value 1 with probability p and value 0 with probability q = 1 − p. The Rademacher distribution, which takes value 1 with probability 1/2 and value −1
List of probability distributions
List_of_probability_distributions
Generalised concept of incidence structure of polygons
In mathematics, a generalized polygon is an incidence structure introduced by Jacques Tits in 1959. Generalized n-gons encompass as special cases projective
Generalized_polygon
Approximation of a function by a polynomial
analysis and mathematical physics. Taylor's theorem also generalizes to multivariate and vector valued functions. It provided the mathematical basis for some
Taylor's_theorem
Probability distribution modeling a coin toss which need not be fair
variable which takes the value 1 with probability p {\displaystyle p} and the value 0 with probability q = 1 − p {\displaystyle q=1-p} . Less formally, it
Bernoulli_distribution
Mathematical statistics distance measure
satisfies a generalized Pythagorean theorem (which applies to squared distances). KL divergence is always a non-negative real number, with value 0 if and
Kullback–Leibler_divergence
Auctioning of sponsored search engine results
auction mechanisms, such as the generalized second-price auction and the Vickrey–Clarke–Groves auction. Generalized second-price auction (GSP) is the
Sponsored_search_auction
Approach in blockmodeling
tie (link) values (or statistical data computed on them) are assumed to be equal (homogenous) within blocks. This approach to the generalized blockmodeling
Homogeneity_blockmodeling
Type of dynamic auction
introducing the common value factor, the English auction has a revenue advantage: each bidder's private information about the common value is valuable information
English_auction
Operation in calculus
of Daniell for the case of real-valued functions on a set X, generalized by Nicolas Bourbaki to functions with values in a locally compact topological
Integral
Study of rates of change
abstract algebra. The theory of derivatives is studied more closely and generalized in subjects such as real analysis, vector calculus, and multivariable
Differential_calculus
Regularization technique for ill-posed problems
regularized problem. For the generalized case, a similar representation can be derived using a generalized singular-value decomposition. Finally, it is
Ridge_regression
Concept in statistics
statistics, the class of vector generalized linear models (VGLMs) was proposed to enlarge the scope of models catered for by generalized linear models (GLMs). In
Vector generalized linear model
Vector_generalized_linear_model
Statistical method for multiple testing
p-values can be produced by transforming the HMP. Generalized central limit theorem shows that an asymptotically exact p-value, p p ∘ {\textstyle p_{\overset
Harmonic_mean_p-value
Type of probability distribution
of values specified for that variable. In the case of only two random variables, this is called a bivariate distribution, but the concept generalizes to
Joint probability distribution
Joint_probability_distribution
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating
Mean_value_theorem
Ethical or philosophic value that an object has "in itself" or "for its own sake"
intrinsic value is a property of anything that is valuable on its own. Intrinsic value is in contrast to instrumental value (also known as extrinsic value), which
Intrinsic_value_(ethics)
Formula in calculus
polynomial remainder theorem (the little Bézout theorem, or factor theorem), generalized to an appropriate class of functions.[citation needed] The full generalization
Chain_rule
Research program
can be generalized to the p-adic numbers. This observation initiated the study of p-adic string theory. Another approach considers particles in a p-adic
P-adic_quantum_mechanics
Income statement with commentary
fluctuation in the value of a portfolio of trades to the root causes of the changes. P&L is the day-over-day change in the value of a portfolio of trades
PnL_explained
Average uncertainty in variable's states
log p ( X ) ] {\displaystyle \mathbb {E} [-\log p(X)]} generalizes the above. The core idea of information theory is that the "informational value" of
Entropy_(information_theory)
distribution with estimated degrees of freedom (df). Use generalized p-values based on generalized test variables. Use Roy's union-intersection principle
Multivariate Behrens–Fisher problem
Multivariate_Behrens–Fisher_problem
Probability distribution
generalized gamma distributions. The gamlss package in R allows for fitting and generating many different distribution families including generalized
Generalized gamma distribution
Generalized_gamma_distribution
Relationship between derivatives and integrals
by James Gregory (1638–1675). Isaac Barrow (1630–1677) proved a more generalized version of the theorem, while his student Isaac Newton (1642–1727) completed
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Function spaces generalizing finite-dimensional p norm spaces
p + | x 2 | p + ⋯ + | x n | p ) 1 / p . {\displaystyle \|x\|_{p}=\left(|x_{1}|^{p}+|x_{2}|^{p}+\dotsb +|x_{n}|^{p}\right)^{1/p}.} The absolute value bars
Lp_space
Correction factor which describes the deviation of a real gas from ideal gas behavior
for Z {\displaystyle Z} values greater than 0.6 and within 4–6 percent for Z {\displaystyle Z} values of 0.3–0.6. The generalized compressibility factor
Compressibility_factor
How many different types are in a dataset
p 1 p 1 ) + ln ( p 2 p 2 ) + ln ( p 3 p 3 ) + ⋯ + ln ( p R p R ) ] = − ln ( p 1 p 1 p 2 p 2 p 3 p 3 ⋯ p R p R ) = ln ( 1 p 1 p 1 p 2 p 2 p 3
Diversity_index
Conjecture about gaps between prime numbers
been stated as an inequality, the generalized Andrica conjecture: p n + 1 x − p n x < 1 {\displaystyle p_{n+1}^{x}-p_{n}^{x}<1} for x < x min . {\displaystyle
Andrica's_conjecture
Function whose values are sets (mathematics)
degree theory. In particular, equations are generalized to inclusions, while differential equations are generalized to differential inclusions. One can distinguish
Set-valued_function
Calculus of vector-valued functions
eigenvalues of the Hessian matrix at these zeros. Vector calculus can also be generalized to other 3-manifolds and higher-dimensional spaces. Vector calculus is
Vector_calculus
Difference between logarithm and harmonic series
Murty and A. Zaytseva showed that the generalized Euler constants have the same property, where the generalized Euler constant are defined as γ ( Ω )
Euler's_constant
Conjecture on zeros of the zeta function
p. 359) say The method of proof here is truly amazing. If the generalized Riemann hypothesis is true, then the theorem is true. If the generalized Riemann
Riemann_hypothesis
Statistical estimation technique
In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model. It is used when there
Generalized_least_squares
Function returning minus 1, zero or plus 1
{\displaystyle (\operatorname {sgn} 0)^{2}=0} . This generalized signum allows construction of the algebra of generalized functions, but the price of such generalization
Sign_function
Probability distribution and special case of gamma distribution
distribution. Just as extreme values of the normal distribution have low probability (and give small p-values), extreme values of the chi-squared distribution
Chi-squared_distribution
Risk measure estimating the average loss in the worst tail of the distribution
{dQ}{dP}}} is the Radon–Nikodym derivative of Q {\displaystyle Q} with respect to P {\displaystyle P} . Expected shortfall can be generalized to a general
Expected_shortfall
Computational problem
winning strategy in a generalized geography game is PSPACE-complete. Let GG = { ⟨G, b⟩ | P1 has a winning strategy for the generalized geography game played
Generalized_geography
Integral of sin(x)/x from 0 to infinity
however, integrable in the sense of the improper Riemann integral or the generalized Riemann or Henstock–Kurzweil integral. This can be seen by using Dirichlet's
Dirichlet_integral
Image edge detection algorithm
pixel above and below it in the vertical axis), the value will be preserved. Otherwise, the value will be suppressed. In some implementations, the algorithm
Canny_edge_detector
Better to receive money now than later
The time value of money refers to the idea that there is generally a greater benefit to receiving a sum of money now rather than an identical sum later
Time_value_of_money
Statement relating differentiable symmetries to conserved quantities
bundle of space of generalized positions. In field theory, M is the spacetime manifold and the target space is the set of values the fields can take
Noether's_theorem
Personal value, basis for ethical action
Abstract exceptions serve to reinforce the ranking of values. Their definitions are generalized enough to be relevant to any and all situations. Situational
Value_(ethics)
Family of continuous probability distributions
special values of the skewed generalized t distribution. The Skewed Generalized Error Distribution (SGED) has the pdf: lim q → ∞ f SGT ( x ; μ , σ , λ , p ,
Skewed generalized t distribution
Skewed_generalized_t_distribution
Diagnostic plot of binary classifier ability
binary classifier model (although it can be generalized to multiple classes) at varying threshold values. ROC analysis is commonly applied in the assessment
Receiver operating characteristic
Receiver_operating_characteristic
Concept in functional programming
version of generalized algebraic data types were described by Augustsson & Petersson (1994) and based on pattern matching in ALF. Generalized algebraic
Generalized algebraic data type
Generalized_algebraic_data_type
Sum of the first n whole number reciprocals; 1/1 + 1/2 + 1/3 + ... + 1/n
does not divide the denominator of generalized harmonic number H(k, n) nor the denominator of alternating generalized harmonic number H′(k, n) is, for n=1
Harmonic_number
Mathematical conjecture about zeros of L-functions
proofs of this without using the generalized Riemann hypothesis. In 1917, Hardy and Littlewood showed that the generalized Riemann hypothesis implies a conjecture
Generalized Riemann hypothesis
Generalized_Riemann_hypothesis
Concept in statistics
response values (dependent variable values) to the vector of fitted values (or predicted values). It describes the influence each response value has on
Projection_matrix
Statistical regression where the dependent variable can take only two values
Logit, Probit, and Other Generalized Linear Models. Sage. ISBN 0-8039-4999-5. McCullagh, Peter; John Nelder (1989). Generalized Linear Models. London: Chapman
Probit_model
Signal processing technique
Generalized pencil-of-function method (GPOF), also known as matrix pencil method, is a signal processing technique for estimating a signal or extracting
Generalized pencil-of-function method
Generalized_pencil-of-function_method
Value that appears most often in a set of data
the probability mass function P(X) takes its maximum value, i.e., x = argmaxxi P(X = xi). In other words, it is the value that is most likely to be sampled
Mode_(statistics)
Symmetric probability distribution
reasonably modeled with a symmetric distribution. The generalized lambda distribution (GLD) generalizes the lambda distribution by splitting the occurrences
Tukey_lambda_distribution
Algorithm for finding a zero of a function
polynomial. The bisection method has been generalized to multi-dimensional functions. Such methods are called generalized bisection methods. Some of these methods
Bisection_method
Value approached by a mathematical object
derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related
Limit_(mathematics)
Mathematical function for the probability a given outcome occurs in an experiment
the event "the die rolls an even value" is P ( 2 ) + P ( 4 ) + P ( 6 ) = 1 6 + 1 6 + 1 6 = 1 2 {\displaystyle P(2)+P(4)+P(6)={\frac {1}{6}}+{\frac {1}{6}}+{\frac
Probability_distribution
Formulation of classical mechanics
{\displaystyle N} generalized coordinates q 1 , q 2 , … , q N {\displaystyle q_{1},\,q_{2},\dots ,q_{N}} and the time t {\displaystyle t} . The generalized momenta
Hamilton–Jacobi_equation
Circulation density in a vector field
value of a vector-valued surface integral around a shell enclosing p divided by the volume enclosed, as the shell is contracted indefinitely around p
Curl_(mathematics)
Fee
for the lot. In Europe, the buyer's premium may also be subject to VAT (value-added tax), while in the United States, most states require sales tax to
Buyer's_premium
Concepts from linear algebra
normal form and therefore admits a basis of generalized eigenvectors and a decomposition into generalized eigenspaces. In the Hermitian case, eigenvalues
Eigenvalues_and_eigenvectors
Matrix decomposition
orthogonal functions (EOFs) Fourier analysis Generalized singular value decomposition Inequalities about singular values K-SVD Latent semantic analysis Latent
Singular_value_decomposition
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GENERALIZED P-VALUE