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Probability distribution
and statistics, the chi distribution is a continuous probability distribution over the non-negative real line. It is the distribution of the positive square
Chi_distribution
Probability distribution and special case of gamma distribution
statistics, the χ 2 {\displaystyle \chi ^{2}} -distribution with k {\displaystyle k} degrees of freedom is the distribution of a sum of the squares of k {\displaystyle
Chi-squared_distribution
Noncentral generalization of the chi-squared distribution
the noncentral chi-squared distribution (or noncentral chi-square distribution, noncentral χ 2 {\displaystyle \chi ^{2}} distribution) is a noncentral
Noncentral chi-squared distribution
Noncentral_chi-squared_distribution
Probability distribution
statistics, the inverse-chi-squared distribution (or inverted-chi-square distribution) is a continuous probability distribution of a positive-valued random
Inverse-chi-squared distribution
Inverse-chi-squared_distribution
Statistical hypothesis test
statistical tests where the chi-squared distribution is approximately valid: For an exact test used in place of the 2 × 2 chi-squared test for independence
Chi-squared_test
Gamma distribution, and it is used in goodness-of-fit tests in statistics. The inverse-chi-squared distribution The noncentral chi-squared distribution The
List of probability distributions
List_of_probability_distributions
Kind of probability distribution
and statistics, the generalized chi-squared distribution (or generalized chi-square distribution) is the distribution of a quadratic function of a multinormal
Generalized chi-squared distribution
Generalized_chi-squared_distribution
Evaluates how likely it is that any difference between data sets arose by chance
statistical procedures whose results are evaluated by reference to the chi-squared distribution. Its properties were first investigated by Karl Pearson in 1900
Pearson's_chi-squared_test
Probability distribution
Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distribution
Rayleigh_distribution
noncentral chi distribution is a noncentral generalization of the chi distribution. It is also known as the generalized Rayleigh distribution. If X i {\displaystyle
Noncentral_chi_distribution
Probability distribution
The scaled inverse chi-squared distribution ψ inv- χ 2 ( ν ) {\displaystyle \psi \,{\mbox{inv-}}\chi ^{2}(\nu )} , where ψ {\displaystyle \psi } is the
Scaled inverse chi-squared distribution
Scaled_inverse_chi-squared_distribution
Statistical distribution
of chi-distribution, similar to a gamma distribution being considered as a generalization of chi-squared distributions. The Nakagami distribution is relatively
Nakagami_distribution
Specific probability distribution function, important in physics
statistical distribution of speeds is derived by equating particle energies with kinetic energy. Mathematically, the Maxwell–Boltzmann distribution is the chi distribution
Maxwell–Boltzmann distribution
Maxwell–Boltzmann_distribution
t-distribution Noncentral chi-squared distribution Noncentral chi-distribution Noncentral F-distribution Noncentral beta distribution In general, noncentrality
Noncentral_distribution
Continuous probability distribution
and U 2 {\textstyle U_{2}} are independent random variables with chi-square distributions with respective degrees of freedom d 1 {\displaystyle d_{1}}
F-distribution
Probability distribution
theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable
Normal_distribution
Two-parameter family of continuous probability distributions
parametrize the inverse gamma distribution differently, as a scaled inverse chi-squared distribution. The inverse gamma distribution's probability density function
Inverse-gamma_distribution
Topics referred to by the same term
Peachy Chi site, a DNA sequence that serves as a recombination hot spot Chi distribution, in statistics Chi, the hyperbolic cosine integral CHI (conference)
Chi
characteristics related to the chi-squared distribution. Let random variable Y be defined as Y = X2 where X has normal distribution with mean 0 and variance
Proofs related to chi-squared distribution
Proofs_related_to_chi-squared_distribution
Generalization of the one-dimensional normal distribution to higher dimensions
p ) {\displaystyle \chi _{k}^{2}(p)} is the quantile function for probability p {\displaystyle p} of the chi-squared distribution with k {\displaystyle
Multivariate normal distribution
Multivariate_normal_distribution
Probability distribution
normal distribution) If Y has a half-normal distribution, then (Y/σ)2 has a chi square distribution with 1 degree of freedom, i.e. Y/σ has a chi distribution
Half-normal_distribution
Probability distribution
distribution is a versatile two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared
Gamma_distribution
Discrete probability distribution
Poisson distribution can be expressed using the relationship between the cumulative distribution functions of the Poisson and chi-squared distributions. The
Poisson_distribution
Twenty-second letter of the Greek alphabet
various uses, including the chi-squared distribution, the chi-squared test, and chi-squared target model In algebraic topology, Chi is used to represent the
Chi_(letter)
Generalization of gamma distribution to multiple dimensions
= 1 then this distribution is a chi-squared distribution with n degrees of freedom. The Wishart distribution arises as the distribution of the sample
Wishart_distribution
Probability distribution
divided by an independent chi-distributed random variable, while the F-distribution originates from the ratio of two independent chi-squared distributed random
Ratio_distribution
Distribution of new data marginalized over the posterior
prior scaled-inverse-chi-squared distribution placed on σx2, with hyperparameters ν and σ2. The resulting compound distribution t ( x | μ , ν , σ 2 )
Posterior predictive distribution
Posterior_predictive_distribution
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
Topics referred to by the same term
The term chi-square, chi-squared, or χ 2 {\displaystyle \chi ^{2}} has various uses in statistics: chi-square distribution, a continuous probability distribution
Chi-square
Measure of variation in statistics
sampling distribution of the sample standard deviation follows a (scaled) chi distribution, and the correction factor is the mean of the chi distribution. An
Standard_deviation
population distribution if a specified test statistic is too large, when that statistic would have approximately a chi-square distribution if the null
Minimum_chi-square_estimation
that the range is. For normal data s is chi distributed and the distribution function fS of the chi distribution is given by: f S ( s ; ν ) d s = { ν ν
Studentized range distribution
Studentized_range_distribution
Probability distribution
theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in
Exponential_distribution
Metric for fit of statistical models
from identical distributions (see Kolmogorov–Smirnov test), or whether outcome frequencies follow a specified distribution (see Pearson's chi-square test)
Goodness_of_fit
"Pushed forward" from one measurable space to another
{\big (}f^{-1}(A){\big )}=0} Many natural probability distributions, such as the chi distribution, can be obtained via this construction. In general, any
Pushforward_measure
Probability distribution used in multivariate hypothesis testing
2(m-p+1)}.} Chi-squared distribution Dirichlet distribution F-distribution Gamma distribution Hotelling's T-squared distribution Student's t-distribution Wishart
Wilks's_lambda_distribution
Mathematical function for the probability a given outcome occurs in an experiment
(see chi-squared test) Student's t distribution, the distribution of the ratio of a standard normal variable and the square root of a scaled chi squared
Probability_distribution
non-central chi-squared distribution with zero degrees of freedom can be used in testing the null hypothesis that a sample is from a uniform distribution on the
Zero_degrees_of_freedom
Statistical theorem
\infty } , the distribution of the test statistic − 2 log ( Λ ) {\displaystyle -2\log(\Lambda )} asymptotically approaches the chi-squared ( χ 2 {\displaystyle
Wilks'_theorem
Topic in probability theory and statistics
A gamma distribution with shape parameter α = v/2 and rate parameter β = 1/2 is a chi-squared distribution with ν degrees of freedom. A chi-squared distribution
Relationships among probability distributions
Relationships_among_probability_distributions
Probability distribution
has a chi-squared distribution (χ2-distribution) with ν {\displaystyle \nu } degrees of freedom; Z and V are independent; A different distribution is defined
Student's_t-distribution
Multivariable generalization of the Student's t-distribution
{\Sigma }})} and χ ν 2 {\displaystyle \chi _{\nu }^{2}} (i.e. multivariate normal and chi-squared distributions) respectively, the matrix Σ {\displaystyle
Multivariate_t-distribution
Leader of North Vietnam from 1945 to 1969
Hồ Chí Minh (born Nguyễn Sinh Cung; 19 May 1890 – 2 September 1969), colloquially known as Uncle Ho (Bác Hồ) among other aliases and sobriquets, was a
Ho_Chi_Minh
Family of continuous probability distributions
2, the distribution simplifies to the chi-squared distribution with 2k degrees of freedom. It can therefore be regarded as a generalized chi-squared
Erlang_distribution
Probability distribution
distribution (Type I) is the distribution of the ratio X = χ m 2 ( λ ) χ m 2 ( λ ) + χ n 2 , {\displaystyle X={\frac {\chi _{m}^{2}(\lambda )}{\chi _{m}^{2}(\lambda
Noncentral_beta_distribution
Three-parameter family of continuous probability distributions
z = a y, where a has a chi distribution and y a complex Gaussian distribution. The modulus of z, |z|, then has K-distribution. The moment generating function
K-distribution
Probability distribution generalizing the F-distribution with a noncentrality parameter
F-distribution. It describes the distribution of the quotient (X/n1)/(Y/n2), where the numerator X has a noncentral chi-squared distribution with n1 degrees of freedom
Noncentral_F-distribution
Probability distribution in physics
distribution is: f ( x ; χ , c ) = χ 3 2 π Ψ ( χ ) ⋅ x c 2 1 − x 2 c 2 exp { − 1 2 χ 2 ( 1 − x 2 c 2 ) } , {\displaystyle f(x;\chi ,c)={\frac {\chi
ARGUS_distribution
Probability distribution
{\displaystyle 2}{b}}\sum _{i=1}^{n}|X_{i}-\mu |\sim \chi ^{2}(2n)} (chi-squared distribution). If X , Y ∼ Laplace ( μ , b ) {\displaystyle X,Y\sim {\textrm
Laplace_distribution
inequality Chernoff face Chernoff's distribution Chernoff's inequality Chi distribution Chi-squared distribution Chi-squared test Chinese restaurant process
List_of_statistics_articles
Procedure to estimate standard deviation from a sample
n − 1 ) s 2 / σ 2 {\displaystyle (n-1)s^{2}/\sigma ^{2}} has a chi square distribution with n − 1 {\displaystyle n-1} degrees of freedom and thus its
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Probability distribution
\beta )\,} . Chi-squared distribution: If X ∼ χ 2 ( α ) {\displaystyle X\sim \chi ^{2}(\alpha )\,} and Y ∼ χ 2 ( β ) {\displaystyle Y\sim \chi ^{2}(\beta
Beta_distribution
Symbols for constants, special functions
normal distribution in statistics the Veblen functions χ {\displaystyle \chi } represents: the chi distribution in statistics ( χ 2 {\displaystyle \chi ^{2}}
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
Probability distribution
distribution (also known as offset normal distribution, angular normal distribution or angular Gaussian distribution) is a probability distribution over
Projected_normal_distribution
Statistical test used on paired nominal data
2 {\displaystyle \chi ^{2}} has a chi-squared distribution with 1 degree of freedom. If the χ 2 {\displaystyle \chi ^{2}} result is significant, this
McNemar's_test
Probability distribution
{\displaystyle X\,\sim \,\operatorname {Scale-inv-\chi ^{2}} (1,c)} (scaled-inverse-chi-squared distribution). If X ∼ Levy ( μ , c ) {\displaystyle X\sim
Lévy_distribution
Statistical measure of how far values spread from their average
theorem shows that the unbiased sample variance S2 follows a scaled chi-squared distribution (see also: asymptotic properties and an elementary proof): ( n
Variance
Continuous probability distribution
positive integer; Chi-Squared distribution, when α = 1 {\displaystyle \alpha =1} and ν = {\displaystyle \nu =} half integer; Nakagami distribution, when α = 2
Kaniadakis_Gamma_distribution
Probability distribution
follows a normal distribution, and that both S 1 2 {\displaystyle S_{1}^{2}} and S 2 2 {\displaystyle S_{2}^{2}} has a chi-squared distribution, which is approximately
Log-normal_distribution
A Chi site or Chi sequence is a short stretch of DNA in the genome of a bacterium near which homologous recombination is more likely to occur than on
Chi_site
Statistical method
The correction modifies the standard chi-squared test to account for the fact that a continuous distribution (chi-squared) is used to approximate discrete
Yates's correction for continuity
Yates's_correction_for_continuity
Measure of inequality of a statistical distribution
November 2022. "Chi-Squared Distribution -- from Wolfram MathWorld". mathworld.wolfram.com. Retrieved 11 January 2023. "Weibull Distribution: Characteristics
Gini_coefficient
Continuous probability distribution
. Erlang distribution, when α = 1 {\displaystyle \alpha =1} and ν = n = {\displaystyle \nu =n=} positive integer; Chi-Squared distribution, when α =
Kaniadakis_distribution
Type of probability distribution
}}-{\boldsymbol {\mathbf {\mu } }})\sim \chi _{p}^{2},} where χ p 2 {\displaystyle \chi _{p}^{2}} is the chi-squared distribution with p degrees of freedom. Alternatively
Hotelling's T-squared distribution
Hotelling's_T-squared_distribution
Type of mathematical distribution
− k = δ ( k − 1 ) . {\displaystyle \chi _{+}^{-k}=\delta ^{(k-1)}.} The distributions χ + a {\displaystyle \chi _{+}^{a}} have the properties d d x χ
Homogeneous_distribution
Family of probability distributions related to the normal distribution
exponential gamma chi-squared beta Dirichlet Bernoulli categorical Poisson Wishart inverse Wishart geometric A number of common distributions are exponential
Exponential_family
American R&B/soul vocal group from Chicago, Illinois
The Chi-Lites (/ˈʃaɪlaɪts/, SHY-lytes) is an American R&B/soul vocal quartet from Chicago. Forming at Chicago's Hyde Park High School in 1959, the group's
The_Chi-Lites
Test statistic
In statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD)
Reduced_chi-squared_statistic
Probability distribution
Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution f (
Cauchy_distribution
Function in statistics
as a complementary cumulative distribution function for noncentral chi, noncentral chi-squared, and Rice distributions. In engineering, this function
Marcum_Q-function
Taiwanese humanitarian nongovernmental organization
The Buddhist Tzu Chi Charity Foundation (Chinese: 佛教慈濟慈善事業基金會; lit. 'Buddhist Compassionate Relief Charitable Foundation') is a Taiwanese international
Tzu_Chi
Probability distribution
statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite
Inverse-Wishart_distribution
Canadian musician and composer (born 1969)
1996) All Systems Go! (Cobraside Distribution, 1999) I'll Be Your Radio (Cobraside Distribution, 2001, EP) Mon Chi Chi (Bad Taste Records, 2002) Fascination
John_Kastner
University in Hualien, Taiwan
Tzu Chi University of Science and Technology (TCUST; Chinese: 慈濟科技大學) is a private university in Hualien City, Hualien County, Taiwan. Tzu Chi University
Tzu Chi University of Science and Technology
Tzu_Chi_University_of_Science_and_Technology
Type of mathematical function
the binomial distribution, the logistic distribution, the extreme value distribution, the Laplace distribution, the chi distribution, the hyperbolic
Logarithmically concave function
Logarithmically_concave_function
Statistical property
error (SE) of a statistic is the standard deviation of its sampling distribution. It is the square root of the variance of an estimator of a parameter
Standard_error
Alleged boss behind Sam Gor crime syndicate
Tse Chi Lop (Chinese: 謝志樂, born 25 October 1963) is a Chinese and Canadian gangster, drug trafficker and drug cartel leader. Before his arrest, Tse was
Tse_Chi_Lop
Fourth standardized moment in statistics
'curved, arching') refers to the degree of tailedness in the probability distribution of a real-valued, random variable in probability theory and statistics
Kurtosis
Non-parametric method for testing whether samples originate from the same distribution
distribution of H {\displaystyle H} can be quite different from this chi-squared distribution. If a table of the chi-squared probability distribution
Kruskal–Wallis_test
Normality test
variance. If the data comes from a normal distribution, the JB statistic asymptotically has a chi-squared distribution with two degrees of freedom, so the statistic
Jarque–Bera_test
(PDF) October 14, 2008 Mercury Export Ban Act To prohibit the sale, distribution, transfer, and export of elemental mercury, and for other purposes. Pub
List of acts of the 110th United States Congress
List_of_acts_of_the_110th_United_States_Congress
278. ISBN 978-1-420-01137-1. Notes More precisely 1.53817..., the square root of the median of a chi-squared distribution with 3 degrees of freedom.
Misconceptions about the normal distribution
Misconceptions_about_the_normal_distribution
Statistical test comparing two probability distributions
empirical distribution function of the sample and the cumulative distribution function of the reference distribution, or between the empirical distribution functions
Kolmogorov–Smirnov_test
American film and television and distribution company
Amazon MGM Studios is an American film and television production and distribution company and the flagship namesake subsidiary of Amazon. Founded as Amazon
Amazon_MGM_Studios
Restaurant disease outbreak
The outbreak was caused by contaminated green onions (scallions) at a Chi-Chi's restaurant at Beaver Valley Mall in Monaca, Pennsylvania, approximately
2003 Chi-Chi's hepatitis A outbreak
2003_Chi-Chi's_hepatitis_A_outbreak
Statistical test used to test homoscedasticity
procedure is based on the statistic whose sampling distribution is approximately a Chi-Square distribution with (k − 1) degrees of freedom, where k is the
Bartlett's_test
Generalization of the binomial distribution
converges in distribution to the chi-squared distribution χ 2 ( k − 1 ) {\displaystyle \chi ^{2}(k-1)} . [Proof] The space of all distributions over categories
Multinomial_distribution
Measure of the asymmetry of random variables
theory and statistics is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. Similarly to kurtosis
Skewness
Concept in statistics
P and Q distributions of an N mode system are as follows: χ W ( z , z ∗ ) = tr [ ρ exp ( i z ⋅ a ^ + i z ∗ ⋅ a ^ † ) ] {\displaystyle \chi _{W}(\mathbf
Quasiprobability_distribution
1993 Hong Kong film by Yuen Woo-ping
Tai Chi Master (Chinese: 太極張三豐), also known as Twin Warriors or simply Tai Chi, is a 1993 Hong Kong martial arts film directed by Yuen Woo-ping, and produced
Tai_Chi_Master_(film)
to the Chi distribution, and is given by P n ( r ) ∝ r n − 1 e − r 2 / 2 {\displaystyle P_{n}(r)\propto r^{n-1}e^{-r^{2}/2}} This distribution is peaked
Multiple-try_Metropolis
Japanese manga series and its adaptations
Chi's Sweet Home (Japanese: チーズスイートホーム, Hepburn: Chīzu Suīto Hōmu) is a Japanese manga series written and illustrated by Konami Kanata. It was serialized
Chi's_Sweet_Home
Statistical distribution of complex random variables
distribution (a complex normal distribution is a bivariate normal distribution) Generalized chi-squared distribution Wishart distribution Complex random variable
Complex_normal_distribution
Equation to approximate pooled degrees of freedom
probability distribution of χ' cannot be expressed analytically. However, its distribution can be approximated by another chi-squared distribution, whose effective
Welch–Satterthwaite_equation
Statistical test
G} is asymptotically chi-squared distributed as the total number of observations tends to infinity (convergence in distribution). Furthermore, the total
G-test
Interference effect in radar systems
number of individual radiators and considering the result using the chi-squared distribution: p ( σ ) = m Γ ( m ) σ a v ( m σ σ a v ) m − 1 e − m σ σ a v I
Fluctuation_loss
This list concerns blood type distribution between countries and regions. Blood type (also called a blood group) is a classification of genes, based on
Blood type distribution by country
Blood_type_distribution_by_country
Statistic used in statistical hypothesis testing
50% proportion). Chi-squared tests use the same calculations and the same probability distribution for different applications: Chi-squared tests for
Test_statistic
Statistical theorem in the analysis of variance
r_{1}+\cdots +r_{k}=N} , the Qi are independent each Qi has a chi-squared distribution with ri degrees of freedom. Often it's stated as ∑ i A i = A {\displaystyle
Cochran's_theorem
1954 film
"Pietà per chi cade" (review). Corriere della Sera. 30 March 1954. Pietà per chi cade at IMDb Pietà per chi cade at Variety Distribution v t e v t e
Pietà_per_chi_cade
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