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・ Inverse distribution
・ Inverse dynamics
・ Inverse electron-demand Diels–Alder reaction
・ Inverse element
・ Inverse exchange-traded fund
・ Inverse Faraday effect
・ Inverse filter
・ Inverse filter (disambiguation)
・ Inverse floating rate note
・ Inverse function
・ Inverse function theorem
・ Inverse functions and differentiation
・ Inverse Galois problem
・ Inverse gambler's fallacy
・ Inverse gas chromatography
Inverse Gaussian distribution
・ Inverse hyperbolic function
・ Inverse image functor
・ Inverse iteration
・ Inverse kinematics
・ Inverse Laplace transform
・ Inverse limit
・ Inverse magnetostrictive effect
・ Inverse mapping theorem
・ Inverse matrix gamma distribution
・ Inverse mean curvature flow
・ Inverse method
・ Inverse Mills ratio
・ Inverse multiplexer
・ Inverse Multiplexing for ATM


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Inverse Gaussian distribution : ウィキペディア英語版
Inverse Gaussian distribution
|
cdf = \Phi\left(\sqrt} \left(\frac-1 \right)\right) +\exp\left(\frac\right) \Phi\left(-\sqrt}\left(\frac+1 \right)\right)
where \Phi \left(\right) is the standard normal (standard Gaussian) distribution c.d.f. |
mean =\scriptstyle \mathbf(X ) = \mu
\scriptstyle \mathbf() = \frac + \frac|
median =|
mode =\mu\left(X ) = \frac
\scriptstyle \mathbf() = \frac + \frac|
skewness =3\left(\frac\right)^ |
kurtosis =\frac |
entropy =|
mgf =e^\right)\left()}|
char =e^\right)\left()}|
}}
In probability theory, the inverse Gaussian distribution (also known as the Wald distribution) is a two-parameter family of continuous probability distributions with support on (0,∞).
Its probability density function is given by
: f(x;\mu,\lambda)
= \left(normal (Gaussian) distribution. The inverse Gaussian distribution has several properties analogous to a Gaussian distribution. The name can be misleading: it is an "inverse" only in that, while the Gaussian describes a Brownian Motion's level at a fixed time, the inverse Gaussian describes the distribution of the time a Brownian Motion with positive drift takes to reach a fixed positive level.
Its cumulant generating function (logarithm of the characteristic function) is the inverse of the cumulant generating function of a Gaussian random variable.
To indicate that a random variable ''X'' is inverse Gaussian-distributed with mean μ and shape parameter λ we write
:X \sim IG(\mu, \lambda).\,\!
==Properties==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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