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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 ...
The inverse Gaussian and gamma distributions are special cases of the generalized inverse Gaussian distribution for p = −1/2 and b = 0, respectively. [7] Specifically, an inverse Gaussian distribution of the form
Many very common probability distributions belong to the class of EDMs, among them are: normal distribution, binomial distribution, Poisson distribution, negative binomial distribution, gamma distribution, inverse Gaussian distribution, and Tweedie distribution.
Download QR code; Print/export ... and it is restricted to this domain in many computer algebra systems. ... Cumulative distribution function
The probability density, cumulative distribution, and inverse cumulative distribution functions of a generalized chi-squared variable do not have simple closed-form expressions. But there exist several methods to compute them numerically: Ruben's method, [ 7 ] Imhof's method, [ 8 ] IFFT method, [ 6 ] ray method, [ 6 ] and ellipse approximation.
The distribution is a special case of the folded normal distribution with μ = 0.; It also coincides with a zero-mean normal distribution truncated from below at zero (see truncated normal distribution)
In probability theory and statistics, an inverse distribution is the distribution of the reciprocal of a random variable. Inverse distributions arise in particular in the Bayesian context of prior distributions and posterior distributions for scale parameters.
Cumulative distribution function for the exponential distribution Cumulative distribution function for the normal distribution. In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable, or just distribution function of , evaluated at , is the probability that will take a value less than or equal to .