In mathematics, the inverse gamma function Γ − 1 ( x ) {\displaystyle \Gamma ^{-1}(x)} is the inverse function of the gamma function. In other words, y...
6 KB (833 words) - 00:19, 7 May 2025
distribution differently, as a scaled inverse chi-squared distribution. The inverse gamma distribution's probability density function is defined over the support...
11 KB (1,632 words) - 09:32, 12 June 2025
Pseudogamma function Hadamard's gamma function Inverse gamma function Lanczos approximation Multiple gamma function Multivariate gamma function p-adic gamma function...
90 KB (13,545 words) - 04:27, 29 July 2025
prefer the (α,λ) parameterization, utilizing the gamma distribution as a conjugate prior for several inverse scale parameters, facilitating analytical tractability...
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In mathematics, the inverse Laplace transform of a function F {\displaystyle F} is a real function f {\displaystyle f} that is piecewise-continuous,...
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In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems...
43 KB (7,178 words) - 19:08, 3 August 2025
the only shades that are unaffected by gamma. To compensate for this effect, the inverse transfer function (gamma correction) is sometimes applied to the...
43 KB (5,360 words) - 19:38, 27 July 2025
If f : X → Y is an ordinary function, then its inverse is the multivalued function Γ f − 1 ⊆ Y × X {\displaystyle \Gamma _{f^{-1}}\ \subseteq \ Y\times...
11 KB (1,432 words) - 11:59, 6 August 2025
function, Polygamma function Incomplete beta function Incomplete gamma function K-function Multivariate gamma function: A generalization of the Gamma...
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\end{aligned}}} The inverse of Φ is known as the normal quantile function, or probit function and may be expressed in terms of the inverse error function as probit...
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In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: ψ ( z ) = d d z ln Γ ( z ) = Γ ′ ( z ) Γ ( z )...
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Student's t-distribution (redirect from Student's t probability density function)
instance of the hypergeometric function. For information on its inverse cumulative distribution function, see quantile function § Student's t-distribution...
55 KB (6,423 words) - 01:28, 22 July 2025
Further, Γ {\displaystyle \Gamma } is the gamma function. The inverse chi-squared distribution is a special case of the inverse-gamma distribution. with shape...
5 KB (394 words) - 21:42, 12 October 2024
quantile function is also called the percentile function (after the percentile), percent-point function, inverse cumulative distribution function (after...
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reciprocal gamma function is the function f ( z ) = 1 Γ ( z ) , {\displaystyle f(z)={\frac {1}{\Gamma (z)}},} where Γ(z) denotes the gamma function. Since...
11 KB (1,467 words) - 18:45, 23 June 2025
Other inverse distributions include inverse-chi-squared distribution inverse-gamma distribution inverse-Wishart distribution inverse matrix gamma distribution...
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root, and function composition to polynomial, exponential, logarithm, and trigonometric functions. They include inverse trigonometric functions, hyperbolic...
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Restriction (mathematics) (redirect from Function restriction)
restriction of a continuous function is continuous. For a function to have an inverse, it must be one-to-one. If a function f {\displaystyle f} is not...
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/x)}{\Gamma _{1}(\alpha )}}.} i.e., the inverse-gamma distribution, where Γ 1 ( ⋅ ) {\displaystyle \Gamma _{1}(\cdot )} is the ordinary Gamma function. The...
20 KB (3,491 words) - 15:44, 5 June 2025
( γ ) ( t ) = W ( t ) + γ t {\displaystyle W^{(\gamma )}(t)=W(t)+\gamma t} , we can define the inverse Gaussian process A t = inf { s > 0 : W ( γ ) ( s...
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Abel discovered elliptic functions by taking the inverse function φ {\displaystyle \varphi } of the elliptic integral function α ( x ) = ∫ 0 x d t ( 1...
16 KB (2,442 words) - 06:46, 17 July 2025
In probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate...
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Sine and cosine (redirect from Sine function)
\Gamma } is the gamma function and ϖ {\displaystyle \varpi } is the lemniscate constant. The inverse function of sine is arcsine or inverse sine, denoted...
56 KB (7,064 words) - 09:28, 28 July 2025
non-negative integer, one has 2F1(z) → ∞. Dividing by the value Γ(c) of the gamma function, we have the limit: lim c → − m 2 F 1 ( a , b ; c ; z ) Γ ( c ) = (...
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gamma function Γp is a generalization of the gamma function. It is useful in multivariate statistics, appearing in the probability density function of...
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Green's function. A Green's function can also be thought of as a right inverse of L. Aside from the difficulties of finding a Green's function for a particular...
43 KB (5,810 words) - 04:19, 21 July 2025
polylogarithm, inverse tangent integral, polygamma function, Riemann zeta function, Dirichlet eta function, and Dirichlet beta function. The Clausen function of order...
31 KB (6,482 words) - 06:52, 8 August 2025
alternative parametrization is given by the inverse-gamma distribution. The probability density function of the scaled inverse chi-squared distribution extends over...
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their 1952 article "Information theory and inverse probability in telecommunication", saying "This function occurs so often in Fourier analysis and its...
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multiplication can be too, which is doubtful). In fact, both this pairing function and its inverse can be computed with finite-state transducers that run in real...
15 KB (2,488 words) - 13:28, 9 August 2025