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逆高斯分布.
逆高斯分布（英语：Inverse Gaussian distribution）的概率密度函数为
![{\displaystyle f(x;\mu ,\lambda )=\left[{\frac {\lambda }{2\pi x^{3))}\right]^{1/2}\exp {\frac {-\lambda (x-\mu )^{2)){2\mu ^{2}x)){\mbox{ for ))x>0.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97bdd23536c90462aa5b730fa46d7d0494a0bec0)
沃德分布（Wald distribution）是μ = λ = 1时的逆高斯分布特例。
当λ趋近于无穷时，逆高斯分布逐渐趋近于高斯分布。逆高斯分布有多项类似于高斯分布的特性。“逆”可能容易引起混淆，其实它的含义是高斯分布描述的是在布朗运动中某一固定时刻的距离分布，而逆高斯分布描述的是到达固定距离所需时间的分布。
参考文献
- 逆高斯分布，作者Raj Chhikara与Leroy Folks
- 系统可靠性理论，作者Marvin Rausand与Arnljot Høyland
外部链接
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| | 离散单变量 | | 有限支集 | |
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| | 无限支集 |
- beta negative binomial
- Borel
- Conway–Maxwell–Poisson
- discrete phase-type
- Delaporte
- extended negative binomial
- Flory–Schulz
- Gauss–Kuzmin
- 几何分布
- 对数分布
- mixed Poisson
- 负二项分布
- Panjer
- parabolic fractal
- 卜瓦松分布
- Skellam
- Yule–Simon
- zeta
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| | 连续单变量 | |
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| | 混合单变量 | |
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| | 联合分布 |
- Discrete:
- Ewens
- multinomial
- Continuous:
- 狄利克雷分布
- multivariate Laplace
- 多元正态分布
- multivariate stable
- multivariate t
- normal-gamma
- 随机矩阵
- LKJ
- 矩阵正态分布
- matrix t
- matrix gamma
- 威沙特分布
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| | 定向统计 |
- 循环单变量定向统计
- 圆均匀分布
- univariate von Mises
- wrapped normal
- wrapped Cauchy
- wrapped exponential
- wrapped asymmetric Laplace
- wrapped Lévy
- 球形双变量
- Kent
- 环形双变量
- bivariate von Mises
- 多变量
- von Mises–Fisher
- Bingham
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| | 退化分布和奇异分布 | |
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| | 其它 |
- Circular
- 复合泊松分布
- elliptical
- exponential
- natural exponential
- location–scale
- Maximum entropy
- Mixture
- Pearson
- Tweedie
- Wrapped
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![{\displaystyle \left[{\frac {\lambda }{2\pi x^{3))}\right]^{1/2}\exp {\frac {-\lambda (x-\mu )^{2)){2\mu ^{2}x))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9e48e38ac346660ea52189856fd1ff297f48effd)
![{\displaystyle \mu \left[\left(1+{\frac {9\mu ^{2)){4\lambda ^{2))}\right)^{\frac {1}{2))-{\frac {3\mu }{2\lambda ))\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/faccc6b138a2e92276195b63131d43ff17aca2c3)
![{\displaystyle e^{\left({\frac {\lambda }{\mu ))\right)\left[1-{\sqrt {1-{\frac {2\mu ^{2}x}{\lambda ))))\right]))](https://wikimedia.org/api/rest_v1/media/math/render/svg/1c50a3e0d098c94c35e0fc5d0387538fabe47e58)
