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Smooth function in statistics
statistics, the variance function is a smooth function that depicts the variance of a random quantity as a function of its mean. The variance function is a measure
Variance_function
Statistical measure of how far values spread from their average
In probability theory and statistics, variance is a measure of dispersion, meaning it is a measure of how far a set of numbers are spread out from their
Variance
Family of probability distributions
the function τ ( θ ) = κ ′ ( θ ) = μ . {\displaystyle \tau (\theta )=\kappa ^{\prime }(\theta )=\mu .} with cumulative function κ(θ). The variance function
Tweedie_distribution
Class of statistical models
response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized
Generalized_linear_model
Probability distribution
function erf ( x ) {\textstyle \operatorname {erf} (x)} gives the probability of a random variable, with normal distribution of mean 0 and variance
Normal_distribution
Property of a model
In statistics and machine learning, the bias–variance tradeoff describes the relationship between a model's complexity, the accuracy of its predictions
Bias–variance_tradeoff
Empirical law on the variance of species in a habitat
Taylor's power law is an empirical law in ecology that relates the variance of the number of individuals of a species per unit area of habitat to the corresponding
Taylor's_law
Programming language concept
chosen variance determines the relationship between, for example, a list of Cats and a list of Animals, or a function returning Cat and a function returning
Type_variance
Measure of frequency stability in clocks and oscillators
The Allan variance (AVAR), also known as two-sample variance, is a measure of frequency stability in clocks, oscillators and amplifiers. It is named after
Allan_variance
Class of probability distributions
NEF, called NEF with quadratic variance function (NEF-QVF) because the variance can be written as a quadratic function of the mean. NEF-QVF are discussed
Natural_exponential_family
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
Standard score Information ratio Omega ratio Sampling (statistics) Variance function Everitt, Brian (1998). The Cambridge Dictionary of Statistics. Cambridge
Coefficient_of_variation
Set of probability distributions
{Var} [Y]=\sigma ^{2}A''(\theta )=\sigma ^{2}V(\mu )\,\!,} with unit variance function V ( μ ) = A ″ ( ( A ′ ) − 1 ( μ ) ) {\displaystyle V(\mu )=A''((A')^{-1}(\mu
Exponential_dispersion_model
Mathematical function
Gaussian functions is a Gaussian, and the convolution of two Gaussian functions is also a Gaussian, with variance being the sum of the original variances: c
Gaussian_function
Mathematical model for stochastic processes
the conditional variance function, V a r ( Y ∣ X ) = σ 2 ( μ ) {\displaystyle {\rm {{Var}(Y\mid X)=\sigma ^{2}(\mu )}}} , as a function of the conditional
Generalized functional linear model
Generalized_functional_linear_model
Measure of variation in statistics
data set or probability distribution is the square root of its variance (the variance being the average of the squared deviations from the mean). A useful
Standard_deviation
Probability distribution
distribution when marginalizing over the variance parameter. Student's t distribution has the probability density function (PDF) given by f ( t ) = Γ ( ν + 1
Student's_t-distribution
Variance of a random variable given value of other variables
econometrics, the conditional variance is also known as the scedastic function or skedastic function. Conditional variances are important parts of autoregressive
Conditional_variance
Fictional organization appearing in comic books published by Marvel Comics
The Time Variance Authority (TVA) is a fictional organization appearing in American comic books published by Marvel Comics. It is depicted as a group of
Time_Variance_Authority
Measure of the error of an estimator
the square root of the variance, known as the standard error. The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs
Mean_squared_error
Probability distribution
(1-\mu )} The accompanying plot of skewness as a function of variance and mean shows that maximum variance (1/4) is coupled with zero skewness and the symmetry
Beta_distribution
Inexact statistical measure
mean and the variance is specified in the form of a variance function giving the variance as a function of the mean. Generally, this function is allowed
Quasi-likelihood
Concept in applied statistics
regression-based or analysis of variance techniques. The aim behind the choice of a variance-stabilizing transformation is to find a simple function ƒ to apply to values
Variance-stabilizing transformation
Variance-stabilizing_transformation
Collection of statistical models
Analysis of variance (ANOVA) is a family of statistical methods used to compare the means of two or more groups by analyzing variance. Specifically, ANOVA
Analysis_of_variance
Statistical property
all its random variables have the same finite variance; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Statistical measure in mathematical model
In statistics, the variance inflation factor (VIF) is the ratio (quotient) of the variance of a parameter estimate when fitting a full model that includes
Variance_inflation_factor
Features that do not change if length or energy scales are multiplied by a common factor
model that asymptotically manifests a variance to mean power law will be required express a variance function that comes within the domain of attraction
Scale_invariance
Continuous probability distribution
The variance-gamma distribution, generalized Laplace distribution or Bessel function distribution is a continuous probability distribution that is defined
Variance-gamma_distribution
Unbiased statistical estimator minimizing variance
minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than
Minimum-variance unbiased estimator
Minimum-variance_unbiased_estimator
Middle quantile of a data set or probability distribution
population with a density function f ( x ) {\displaystyle f(x)} is asymptotically normal with mean m {\displaystyle m} and variance 1 4 n f ( m ) 2 {\displaystyle
Median
Measure of covariance of components of a random vector
matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between
Covariance_matrix
Probability distribution
diverge to infinity even faster than sample variance. If a probability distribution has a density function f ( x ) {\displaystyle f(x)} , then the mean
Cauchy_distribution
Measure of the shape of a function
inertia. If the function is a probability distribution, then the first moment is the expected value, the second central moment is the variance, the third standardized
Moment_(mathematics)
Method of data analysis
original variables that explains the most variance. The second principal component explains the most variance in what is left once the effect of the first
Principal_component_analysis
Form of global sensitivity analysis
Variance-based sensitivity analysis (often referred to as the Sobol’ method or Sobol’ indices, after Ilya M. Sobol’) is a form of global sensitivity analysis
Variance-based sensitivity analysis
Variance-based_sensitivity_analysis
Function related to statistics and probability theory
A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability
Likelihood_function
Probability distribution
Y do not have the same probability p, then the variance of the sum will be smaller than the variance of a binomial variable distributed as B(n + m, p)
Binomial_distribution
Measure of linear correlation
ratio of two variances Mean cross-product of standardized variables Function of the angle between two standardized regression lines Function of the angle
Pearson correlation coefficient
Pearson_correlation_coefficient
Family of statistical methods based on sampling of available data
package 'samplingVarEst': Sampling Variance Estimation. Implements functions for estimating the sampling variance of some point estimators. Paired
Resampling_(statistics)
Function in probability theory
_{i=1}^{N}\sum _{j=1}^{N}w_{i}C(x_{i},x_{j})w_{j}.} A function is a valid covariance function if and only if this variance is non-negative for all possible choices
Covariance_function
Effect of variables' uncertainties on the uncertainty of a function based on them
{J} ^{\top }.} That is, the Jacobian of the function is used to transform the rows and columns of the variance-covariance matrix of the argument. Note this
Propagation_of_uncertainty
Method of estimating the parameters of a statistical model, given observations
the random errors are assumed to have normal distributions with the same variance. From the perspective of Bayesian inference, MLE is generally equivalent
Maximum_likelihood_estimation
Set of statistical processes for estimating the relationships among variables
quartet Curve fitting Estimation theory Forecasting Fraction of variance unexplained Function approximation Generalized linear model Kriging (a linear least
Regression_analysis
Probability that random variable X is less than or equal to x
cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle X} ,
Cumulative distribution function
Cumulative_distribution_function
Fundamental theorem in probability theory and statistics
each with zero mean and unit variance ( var ( Y ) = 1 {\textstyle \operatorname {var} (Y)=1} ). The characteristic function of Z n {\textstyle Z_{n}} is
Central_limit_theorem
Sales variance is the difference between actual sales and budgeted sales. It is used to measure the performance of a sales function, and/or analyze business
Sales_variance
Mathematical relation assigning a probability event to a cost
optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one
Loss_function
Statistical function that defines the quantiles of a probability distribution
the quantile function of a probability distribution is the inverse of its cumulative distribution function. That is, the quantile function of a distribution
Quantile_function
Statistical property
loss-functions. Any minimum-variance mean-unbiased estimator minimizes the risk (expected loss) with respect to the squared-error loss function (among
Bias_of_an_estimator
Concept in probability theory and statistics
{\displaystyle W} are not independent. The variance is defined in terms of absolute squares as: Properties The variance is always a nonnegative real number.
Complex_random_variable
Description of continuous random distribution
probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function whose value at any given
Probability_density_function
Measure of the joint variability
L2 inner product of real-valued functions on the sample space. As a result, for random variables with finite variance, the inequality | cov ( X , Y
Covariance
Concept in mathematical modelling
given data set. Often, variation is quantified as variance; then, the more specific term explained variance can be used. The complementary part of the total
Explained_variation
Statistical noise
In statistics, the fraction of variance unexplained (FVU) in the context of a regression task is the fraction of variance of the regressand (dependent variable)
Fraction of variance unexplained
Fraction_of_variance_unexplained
Uniform distribution on an interval
terms of mean μ {\displaystyle \mu } and variance σ 2 , {\displaystyle \sigma ^{2},} the probability density function of the continuous uniform distribution
Continuous uniform distribution
Continuous_uniform_distribution
Correlation of a signal with a time-shifted copy of itself, as a function of shift
{\displaystyle \mu } and the variance σ 2 {\displaystyle \sigma ^{2}} are time-independent, and further the autocovariance function depends only on the lag
Autocorrelation
Statistical property quantifying how much a collection of data is spread out
statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data
Statistical_dispersion
Algorithm in computational quantum physics
energy-minimized wave functions on average yield more accurate values of other expectation values than variance minimized wave functions do. The optimization
Variational_Monte_Carlo
Criterion applied in hierarchical cluster analysis
hierarchical cluster analysis. Ward's minimum variance method is a special case of the objective function approach originally presented by Joe H. Ward
Ward's_method
When variance is a random variable
\sigma } with a function ν t {\displaystyle \nu _{t}} that models the variance of S t {\displaystyle S_{t}} . This variance function is also modeled as
Stochastic_volatility
Statistical hypothesis test
t-tests, though strictly speaking that name should only be used if the variances of the two populations are also assumed to be equal; the form of the test
Student's_t-test
Mathematical function having a characteristic "bell"-shaped curve
decreasing variance that approach the Dirac delta distribution. Indeed, the Dirac delta can roughly be thought of as a bell curve with variance tending to
Bell-shaped_function
Procedure for comparing multivariate sample means
In statistics, multivariate analysis of variance (MANOVA) is a procedure for comparing multivariate sample means. As a multivariate procedure, it is used
Multivariate analysis of variance
Multivariate_analysis_of_variance
Statistical hypothesis test
statistical test that compares variances. It is used to determine if the variances of two samples, or if the ratios of variances among multiple samples, are
F-test
Method used in statistics, pattern recognition, and other fields
between groups and the function. Another popular measure of effect size is the percent of variance[clarification needed] for each function. This is calculated
Linear_discriminant_analysis
Important algorithms in numerical statistics
Algorithms for calculating variance play a major role in computational statistics. A key difficulty in the design of good algorithms for this problem is
Algorithms for calculating variance
Algorithms_for_calculating_variance
Statistical test of whether two populations have equal means
Welch's t-test, or unequal variances t-test in statistics is a two-sample location test which is used to test the (null) hypothesis that two populations
Welch's_t-test
Signal with equal energy per octave
"Asymptotic behaviour of the variance function". Scandinavian Journal of Statistics. 21: 223–243. Taylor LR (1961). "Aggregation, variance and the mean". Nature
Pink_noise
Family of solutions to related differential equations
Bessel functions are a class of special functions that commonly appear in problems involving wave motion, heat conduction, and other physical phenomena
Bessel_function
Theorem in portfolio theory
then implications for the functioning of asset markets can be derived and tested. Portfolios can be analyzed in a mean-variance framework, with every investor
Mutual fund separation theorem
Mutual_fund_separation_theorem
Lower bound on variance of an estimator
distribution according to some probability density function f ( x ; θ ) {\displaystyle f(x;\theta )} . The variance of any unbiased estimator θ ^ {\displaystyle
Cramér–Rao_bound
Branch of statistics mathematics
_{0}+\int _{0}^{1}X^{c}(t)\beta (t)\,dt} ; [systematic component] Variance function Var ( Y | X ) = V ( μ ) {\displaystyle {\text{Var}}(Y|X)=V(\mu )}
Functional_data_analysis
Statistical measure of variability
estimator of scale than the sample variance or standard deviation, it works better with distributions without a mean or variance, such as the Cauchy distribution
Median_absolute_deviation
Machine learning paradigm
function (classifier or regression function). If the true function is simple, then an "inflexible" learning algorithm with high bias and low variance
Supervised_learning
Probability distribution
mean zero and variance one, and V {\displaystyle V} is continuously distributed on the positive half-axis with probability density function g {\displaystyle
Normal_variance-mean_mixture
Covariance and correlation
y)} Caution must be applied when using cross correlation function which assumes Gaussian variance for nonlinear systems. In certain circumstances, which
Cross-correlation
Mathematical function for the probability a given outcome occurs in an experiment
density function has a local peak. Quantile: the q-quantile is the value x {\displaystyle x} such that P ( X < x ) = q {\displaystyle P(X<x)=q} . Variance: the
Probability_distribution
Probability distribution
F.; F. L. Cumbrera (August 1997). "The Use of the Pseudo-Voigt Function in the Variance Method of X-ray Line-Broadening Analysis". Journal of Applied Crystallography
Voigt_profile
Procedure to estimate standard deviation from a sample
digital filter), for several settings of α as a function of sample size n. Changing α alters the variance reduction ratio of the filter, which is known
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Discrete-variable probability distribution
and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the probability that a
Probability_mass_function
Statistical method
estimated from the data. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, etc.) to sample estimates. This
Bootstrapping_(statistics)
Probability distribution modeling a coin toss which need not be fair
1+\Pr(X{=}0)\cdot 0\\[1ex]&=p\cdot 1+q\cdot 0\\[1ex]&=p.\end{aligned}}} The variance of a Bernoulli distributed X {\displaystyle X} is Var [ X ] = p q = p
Bernoulli_distribution
Set of quantities in probability theory
μ and variance σ2, the cumulant generating function is K(t) = μt + σ2t2/2. The first and second derivatives of the cumulant generating function are K′(t)
Cumulant
Generalization of the one-dimensional normal distribution to higher dimensions
X i {\displaystyle X_{i}} are independent and each is a zero-mean unit-variance normally distributed random variable, i.e. if X i ∼ N ( 0 , 1 ) {\displaystyle
Multivariate normal distribution
Multivariate_normal_distribution
Concept in statistics
typically the logarithm, which is known as the canonical link. The variance function is proportional to the mean: Var ( Y i ) = τ μ i , {\displaystyle
Vector generalized linear model
Vector_generalized_linear_model
Linear regression model with a single explanatory variable
finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent
Simple_linear_regression
Method for estimating variance of several different populations
In statistics, pooled variance (also known as combined variance, composite variance, or overall variance, and written σ 2 {\displaystyle \sigma ^{2}} )
Pooled_variance
Loss function used in robust regression
sensitivity of the mean-unbiased, minimum-variance estimator of the mean (using the quadratic loss function) and the robustness of the median-unbiased
Huber_loss
Criterion for model selection
The BIC is an increasing function of the error variance σ e 2 {\displaystyle \sigma _{e}^{2}} and an increasing function of k. That is, unexplained
Bayesian information criterion
Bayesian_information_criterion
Rule for calculating an estimate of a given quantity based on observed data
low variance means the arrows are clustered. Even if the variance is low, the cluster of arrows may still be far off-target, and even if the variance is
Estimator
Statistical property
has its own mean and variance. Mathematically, the variance of the sampling mean distribution obtained is equal to the variance of the population divided
Standard_error
Experimental design that is optimal with respect to some statistical criterion
which is related to the variance-matrix of the estimator. Specifying an appropriate model and specifying a suitable criterion function both require understanding
Optimal_experimental_design
Approximation method in statistics
cases. Polynomial least squares describes the variance in a prediction of the dependent variable as a function of the independent variable and the deviations
Least_squares
Statistical modeling method
the following two broad categories: If the goal is to reduce error, i.e. variance in prediction or forecasting, linear regression can be used to fit a predictive
Linear_regression
Two-parameter family of continuous probability distributions
distribution arises as the marginal posterior distribution for the unknown variance of a normal distribution, if an uninformative prior is used, and as an
Inverse-gamma_distribution
Statistical model for a binary dependent variable
concerned with partitioning variance via the sum of squares calculations – variance in the criterion is essentially divided into variance accounted for by the
Logistic_regression
Mathematical framework for investment risk
Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return
Modern_portfolio_theory
Measure of the asymmetry of random variables
distributions converge to a normal distribution with mean 0 and variance 6 (Fisher, 1930). The variance of the sample skewness is thus approximately 6 / n {\displaystyle
Skewness
Estimator for quality of a statistical model
(with zero mean), then the model has three parameters: b0, b1, and the variance of the Gaussian distributions. Thus, when calculating the AIC value of
Akaike_information_criterion
Flaw in mathematical modelling
regression function can be split into random noise, approximation bias, and variance in the estimate of the regression function. The bias–variance tradeoff
Overfitting
Time series model
the variance of the current error term or innovation as a function of the actual sizes of the previous time periods' error terms; often the variance is
Autoregressive conditional heteroskedasticity
Autoregressive_conditional_heteroskedasticity
VARIANCE FUNCTION
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VARIANCE FUNCTION