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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
Probability distribution
probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable
Normal_distribution
Generalization of the one-dimensional normal distribution to higher dimensions
normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution
Multivariate normal distribution
Multivariate_normal_distribution
variables. The generalized logistic distribution The generalized normal distribution The geometric stable distribution The Gumbel distribution The Holtsmark
List of probability distributions
List_of_probability_distributions
Probability distribution
and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness
Skew_normal_distribution
Probability distribution
given set of data. Another example is the half-normal distribution. The generalized gamma distribution has two shape parameters, d > 0 {\displaystyle
Generalized gamma distribution
Generalized_gamma_distribution
Family of distributions that generalize the multivariate normal distribution
elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. In the simplified
Elliptical_distribution
Probability distribution and special case of gamma distribution
standard normal random variables. The chi-squared distribution χ k 2 {\displaystyle \chi _{k}^{2}} is a special case of the gamma distribution and the
Chi-squared_distribution
Kind of probability distribution
theory and statistics, the generalized chi-squared distribution (or generalized chi-square distribution) is the distribution of a quadratic function of
Generalized chi-squared distribution
Generalized_chi-squared_distribution
Probability distribution
The folded normal distribution is a probability distribution related to the normal distribution. Given a normally distributed random variable X with mean
Folded_normal_distribution
Probability distribution
Consequently, the Laplace distribution has fatter tails than the normal distribution. It is a special case of the generalized normal distribution and the hyperbolic
Laplace_distribution
Probability distribution
the half-normal distribution is a special case of the folded normal distribution. Let X {\displaystyle X} follow an ordinary normal distribution, N ( 0
Half-normal_distribution
Family of continuous probability distributions
and statistics, the skewed generalized "t" distribution is a family of continuous probability distributions. The distribution was first introduced by Panayiotis
Skewed generalized t distribution
Skewed_generalized_t_distribution
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
Continuous probability distribution
be generalized hyperbolic at another point in time. In fact, the generalized Laplace distributions and the normal inverse Gaussian distributions are
Generalised hyperbolic distribution
Generalised_hyperbolic_distribution
Name for several different families of probability distributions
The term generalized logistic distribution is used as the name for several different families of probability distributions. For example, Johnson et al
Generalized logistic distribution
Generalized_logistic_distribution
Statistical distribution of complex random variables
In probability theory, the family of complex normal distributions, denoted C N {\displaystyle {\mathcal {CN}}} or N C {\displaystyle {\mathcal {N}}_{\mathcal
Complex_normal_distribution
Type of probability distribution
In probability and statistics, the truncated normal distribution is the probability distribution derived from that of a normally distributed random variable
Truncated_normal_distribution
Continuous probability distribution
The normal-inverse Gaussian distribution (NIG, also known as the normal-Wald distribution) is a continuous probability distribution that is defined as
Normal-inverse Gaussian distribution
Normal-inverse_Gaussian_distribution
Family of continuous probability distributions
statistics, the generalized inverse Gaussian distribution (GIG) is a three-parameter family of continuous probability distributions with probability
Generalized inverse Gaussian distribution
Generalized_inverse_Gaussian_distribution
Probability distribution
continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However
Student's_t-distribution
Probability distribution
the generalized beta distribution is a continuous probability distribution with four shape parameters, including more than thirty named distributions as
Generalized_beta_distribution
Family of probability distributions
theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value
Generalized extreme value distribution
Generalized_extreme_value_distribution
Family of multivariate continuous probability distributions
probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate
Normal-inverse-gamma distribution
Normal-inverse-gamma_distribution
Probability distribution
If instead one normalizes generalized gamma variates, one obtains variates from the simplicial generalized beta distribution (SGB). On the other hand,
Dirichlet_distribution
Probability distribution
the projected normal distribution (also known as offset normal distribution, angular normal distribution or angular Gaussian distribution) is a probability
Projected_normal_distribution
Statistician
Multivariate t-distributions and their applications (2004) Handbook of beta distribution and its applications (2004) A generalized normal distribution (2005)
Saralees_Nadarajah
Particular case of the generalized extreme value distribution
the distribution of the underlying sample data is of the normal or exponential type. The Gumbel distribution is a particular case of the generalized extreme
Gumbel_distribution
Probability distribution
the ratio Z = X/Y is a ratio distribution. An example is the Cauchy distribution (also called the normal ratio distribution), which comes about as the ratio
Ratio_distribution
Continuous probability distribution
the normal distribution in shape but has heavier tails (higher kurtosis). The logistic distribution is a special case of the Tukey lambda distribution. The
Logistic_distribution
Type of probability distribution
"Tables of Quantiles of the Distribution of the Empirical Chiral Index in the Case of the Uniform Law and in the Case of the Normal Law". arXiv:2005.09960
Symmetric probability distribution
Symmetric_probability_distribution
Probability distribution
use, and includes all distributions encompassed by the alternative definitions, as well as those distributions such as log-normal that possess all their
Heavy-tailed_distribution
probability theory and statistics, the generalized multivariate log-gamma (G-MVLG) distribution is a multivariate distribution introduced by Demirhan and Hamurkaroglu
Generalized multivariate log-gamma distribution
Generalized_multivariate_log-gamma_distribution
Mathematical function for the probability a given outcome occurs in an experiment
variables with any distribution: for be any cumulative distribution function F, let Finv be the generalized left inverse of F , {\displaystyle F,} also known
Probability_distribution
Probability distribution
{\displaystyle k} degrees of freedom chi distribution is a special case of various distributions: generalized gamma, Nakagami, noncentral chi, etc. lim
Chi_distribution
Family of probability distributions
Tweedie distributions are a family of probability distributions which include the purely continuous normal, gamma and inverse Gaussian distributions, the
Tweedie_distribution
Statistical model
In statistics, a generalized linear mixed model (GLMM) is an extension to the generalized linear model (GLM) in which the linear predictor contains random
Generalized linear mixed model
Generalized_linear_mixed_model
Distribution of variables which satisfies a stability property under linear combinations
panel). Stable distributions have 0 < α ≤ 2 {\displaystyle 0<\alpha \leq 2} , with the upper bound corresponding to the normal distribution, and approaches
Stable_distribution
Type of probability distribution
distribution function. Note that the formulae here reduce to the case of a finite or infinite mixture if the density w is allowed to be a generalized
Mixture_distribution
Fourth standardized moment in statistics
normal curve'. Excess kurtosis, typically compared to a value of 0, characterizes the tailedness of a distribution. A univariate normal distribution has
Kurtosis
Probability distribution
distribution and normal distribution. (See the previous section.) The Pareto distribution is a special case of the generalized Pareto distribution, which is
Pareto_distribution
Probability distribution
Wishart distribution, and is used similarly, e.g. as the conjugate prior of the covariance matrix of a multivariate normal distribution or matrix normal distribution
Inverse matrix gamma distribution
Inverse_matrix_gamma_distribution
Continuous probability distribution for a non-negative random variable
similar in shape to the log-normal distribution but has heavier tails . Unlike the log-normal, its cumulative distribution function can be written in closed
Log-logistic_distribution
Probability distribution
exponential distribution as one of its members, but also includes many other distributions, such as the normal, binomial, gamma, and Poisson distributions. The
Exponential_distribution
Probability that random variable X is less than or equal to x
discussing general distributions: some specific distributions have their own conventional notation, for example the normal distribution uses Φ {\displaystyle
Cumulative distribution function
Cumulative_distribution_function
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
Probability distribution
natural extension of the normal Gaussian distribution for modeling of long tail data. A Bates distribution that has been generalized as previously stated
Bates_distribution
Generalization of gamma distribution
Wishart distribution, and is used similarly, e.g. as the conjugate prior of the precision matrix of a multivariate normal distribution and matrix normal distribution
Matrix_gamma_distribution
Risk measure estimating the average loss in the worst tail of the distribution
is the standard t-distribution quantile. If the loss of a portfolio L {\displaystyle L} follows generalized Student's t-distribution, the expected shortfall
Expected_shortfall
Probability distribution
The gamma distribution is a special case of the generalized gamma distribution, the generalized integer gamma distribution, and the generalized inverse
Gamma_distribution
Specialized form of regression analysis, in statistics
of regression models is to replace the normal distribution with a heavy-tailed distribution. A t-distribution with 4–6 degrees of freedom has been reported
Robust_regression
Objects that generalize functions
In mathematical analysis, distributions are a type of generalized function that makes it possible to differentiate functions whose derivatives do not
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
logistic distribution Generalized method of moments Generalized multidimensional scaling Generalized multivariate log-gamma distribution Generalized normal distribution
List_of_statistics_articles
Probability distribution
Normal distribution Multimodal distribution Poisson distribution Dorp, J. René van; Kotz, Samuel (March 2003). "Generalized Trapezoidal Distributions". Metrika
Trapezoidal_distribution
Comparison of two distributions
represents N−1(F(x)), where N−1(.) represents the inverse cumulative normal distribution function. The points plotted in a Q–Q plot always have a positive
Q–Q_plot
Fundamental theorem in probability theory and statistics
appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution. This holds even if the original
Central_limit_theorem
Mathematical decision rule
several examples of such alternatives. We denote the posterior generalized distribution function by F {\displaystyle F} . A "linear" loss function, with
Bayes_estimator
Family of continuous probability distributions
LaplacesDemon, and statmod. Generalized inverse Gaussian distribution Tweedie distribution – The inverse Gaussian distribution is a member of the family
Inverse_Gaussian_distribution
Statistical hypothesis test
Student's t-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value
Student's_t-test
Probability distribution
few stable distributions with a probability density function that can be expressed analytically, the others being the normal distribution and the Lévy
Cauchy_distribution
Continuous probability distribution
\nu } ) deformation of the generalized Gamma distribution. The κ-Gamma distribution becomes a ... κ-Exponential distribution of Type I when α = ν = 1 {\displaystyle
Kaniadakis_distribution
Symmetric probability distribution
modeled with a symmetric distribution. The generalized lambda distribution (GLD) generalizes the lambda distribution by splitting the occurrences of λ in the
Tukey_lambda_distribution
Continuous probability distribution
distribution, generalized Laplace distribution or Bessel function distribution is a continuous probability distribution that is defined as the normal
Variance-gamma_distribution
Concept in statistics
commonly modeled using the Poisson distribution, whose variance is equal to its mean. The distribution may be generalized by allowing for variability in its
Compound probability distribution
Compound_probability_distribution
Discrete probability distribution
→ ∞ {\displaystyle n\to \infty } , where a generalized binomial distribution is defined as a distribution of the sum of N independent but not identically
Poisson_distribution
Statistical quantity
2}}} where β > 0 is the rate parameter. Here S is always > 0. Generalized normal distribution version 2 S = − exp ( − k 2 2 ) − 1 exp ( k 2 2 ) − 1 {\displaystyle
Nonparametric_skew
Probability distribution
noncentral t-distribution generalizes Student's t-distribution using a noncentrality parameter. Whereas the central probability distribution describes how
Noncentral_t-distribution
Probability distribution modeling a coin toss which need not be fair
statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which
Bernoulli_distribution
Statistics function
the tail distribution function of the standard normal distribution. In other words, Q ( x ) {\displaystyle Q(x)} is the probability that a normal (Gaussian)
Q-function
Generalization of gamma distribution to multiple dimensions
Bayesian statistics, the Wishart distribution is the conjugate prior of the inverse covariance-matrix of a multivariate-normal random vector. Suppose G is
Wishart_distribution
Basic method for pseudo-random number sampling
cumulative distribution function F {\displaystyle F} of a random variable. For example, imagine that F {\displaystyle F} is the standard normal distribution with
Inverse_transform_sampling
Statistical measure of variability
Analogously to how the median generalizes to the geometric median (GM) in multivariate data, MAD can be generalized to the median of distances to GM
Median_absolute_deviation
Measure of variation in statistics
equations by the lowercase Greek letter σ (sigma). In the case of a normal distribution (as typified by the symmetrical bell-shaped curve), approximately
Standard_deviation
Concept in probability theory
between them, is found in the normal variance-mean mixture, with the generalized inverse Gaussian as conjugate mixing distribution. CG ( ) {\displaystyle
Conjugate_prior
Measure of goodness of fit for a statistical model
)=2\left(y\log {\frac {y}{\mu }}-y+\mu \right)} , the unit deviance for the normal distribution with unit variance is given by d ( y , μ ) = ( y − μ ) 2 {\displaystyle
Deviance_(statistics)
Statistical linear model
and follow a multivariate normal distribution. If the errors do not follow a multivariate normal distribution, generalized linear models may be used to
General_linear_model
parametric assumptions (by using the randomization distribution, without using a normal distribution for the error). In the RCBD, the block-treatment interaction
Generalized randomized block design
Generalized_randomized_block_design
Second theorem in extreme value theory
\infty } converge to a non-degenerate distribution, then such limit is equal to the generalized Pareto distribution: F u ( a ( u ) y + b ( u ) ) → G k
Pickands–Balkema–De Haan theorem
Pickands–Balkema–De_Haan_theorem
Continuous probability distribution
Johnson et al. (1995) places this distribution in the context of a class of generalized forms of the logistic distribution, but use a different parameterisation
Hyperbolic secant distribution
Hyperbolic_secant_distribution
Probability distribution of the possible sample outcomes
mean. The distribution of these means, or averages, is called the "sampling distribution of the sample mean". This distribution is normal N ( μ , σ 2
Sampling_distribution
Statistical test comparing two probability distributions
of testing for normality of the distribution, samples are standardized and compared with a standard normal distribution. This is equivalent to setting
Kolmogorov–Smirnov_test
Probability distribution
{\boldsymbol {\Sigma }}} is the covariance matrix. Unlike the multivariate normal distribution, even if the covariance matrix has zero covariance and correlation
Multivariate Laplace distribution
Multivariate_Laplace_distribution
Measure of the asymmetry of random variables
skewness of 0 A half-normal distribution has a skewness just below 1 An exponential distribution has a skewness of 2 A lognormal distribution can have a skewness
Skewness
Diagnostic plot of binary classifier ability
illustrates the performance of a binary classifier model (although it can be generalized to multiple classes) at varying threshold values. ROC analysis is commonly
Receiver operating characteristic
Receiver_operating_characteristic
Probability distribution
probability theory, the Rice distribution or Rician distribution (or, less commonly, Ricean distribution) is the probability distribution of the magnitude of a
Rice_distribution
Family of functions to transform data
transformation technique used to stabilize variance, make the data more normal distribution-like, improve the validity of measures of association (such as the
Power_transform
Value that appears most often in a set of data
normal distribution, but it may be very different in highly skewed distributions. The mode is not necessarily unique in a given discrete distribution
Mode_(statistics)
Generalization of Gaussian distribution
distribution more suitable than Gaussian distribution to model the effect of external stochasticity. A generalized q-analog of the classical central limit
Q-Gaussian_distribution
Statistical modeling method
where the errors are modeled as normal random variables, there is a close connection between mixed models and generalized least squares. Fixed effects estimation
Linear_regression
Smooth function in statistics
it is likely that the response follows a distribution that is a member of the exponential family, a generalized linear model may be more appropriate to
Variance_function
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
standard normal distributions, i.e., normal distributions with mean 0, variance 1. The noncentral chi-squared distribution generalizes this to normal distributions
Noncentral_distribution
Middle quantile of a data set or probability distribution
symmetrized distribution and which is close to the population median. The Hodges–Lehmann estimator has been generalized to multivariate distributions. The Theil–Sen
Median
Statistic which divides a data set into 100 parts and analyzes it as a percentage
populations following a normal distribution, percentiles may often be represented by reference to a normal curve plot. The normal distribution is plotted along
Percentile
Statistical model for count data
distribution. This model is popular because it models the Poisson heterogeneity with a gamma distribution. Poisson regression models are generalized linear
Poisson_regression
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
approximately log-normal distribution. In such cases, a more accurate estimate, derived from the properties of the log-normal distribution, is defined as:
Coefficient_of_variation
Class of statistical tests
normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying
Normality_test
Mathematical function having a characteristic "bell"-shaped curve
include: Gaussian function, the probability density function of the normal distribution. This is the archetypal bell shaped function and is frequently encountered
Bell-shaped_function
Statistical test
the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution. Z-test tests the mean of a distribution. For
Z-test
Probability distribution
matrix of a multivariate normal distribution. We say X {\displaystyle \mathbf {X} } follows an inverse Wishart distribution, denoted as X ∼ W − 1 ( Ψ
Inverse-Wishart_distribution
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GENERALIZED NORMAL-DISTRIBUTION
GENERALIZED NORMAL-DISTRIBUTION
GENERALIZED NORMAL-DISTRIBUTION
GENERALIZED NORMAL-DISTRIBUTION
GENERALIZED NORMAL-DISTRIBUTION
GENERALIZED NORMAL-DISTRIBUTION
GENERALIZED NORMAL-DISTRIBUTION
GENERALIZED NORMAL-DISTRIBUTION
GENERALIZED NORMAL-DISTRIBUTION
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