`scipy.stats._continuous_distns:norminvgauss_gen`

source: /scipy/stats/_continuous_distns.py:5468

Signature

class norminvgauss_gen(momtype = 1, a = None, b = None, xtol = 1e-14, badvalue = None, name = None, longname = None, shapes = None, seed = None)

Members

Summary

A Normal Inverse Gaussian continuous random variable.

Extended Summary

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Notes

The probability density function for norminvgauss is:

f (x, a, b) = \frac{a K _{1} ( a 1 + x ^{2} )}{π 1 + x ^{2}} exp (a^{2} - b^{2} + b x)

where $x$ is a real number, the parameter $a$ is the tail heaviness and $b$ is the asymmetry parameter satisfying $a > 0$ and $∣ b ∣ <= a$ . $K_{1}$ is the modified Bessel function of second kind (scipy.special.k1).

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A normal inverse Gaussian random variable Y with parameters a and b can be expressed as a normal mean-variance mixture: Y = b * V + sqrt(V) * X where X is norm(0,1) and V is invgauss(mu=1/sqrt(a**2 - b**2)). This representation is used to generate random variates.

Another common parametrization of the distribution (see Equation 2.1 in ^[2]) is given by the following expression of the pdf:

g (x, α, β, δ, μ) = \frac{α δ K _{1} ( α δ ^{2} + ( x - μ ) ^{2} )}{π δ ^{2} + ( x - μ ) ^{2}} e^{δ α^{2} - β^{2} + β (x - μ)}

In SciPy, this corresponds to $a = α δ, b = β δ, loc = μ, scale = δ$ .

Aliases

scipy.stats._continuous_distns.norminvgauss_gen