Inverse Gaussian distribution

This implementation uses the same parameterization as the SciPy implementation in scipy.stats.invgauss, except the shape parameter is called m instead of mu, to avoid confusion with the common use of mu in other parametrizations. loc and scale are the standard location and scale parameters.

A slightly different parametrization is more commonly used (e.g. the Wikipedia article “Inverse Gaussian distribion” [1], NumPy’s numpy.random.Generator.wald, Wolfram Alpha’s InverseGaussianDistribution). (The parameters μ and λ of the Wikipedia article and Wolfram are the same as the mean and scale parameters of NumPy’s wald distribution, respectively.)

To convert from the mpsci parametrization (m, loc, scale) to the more common one, loc must be 0. Then:

μ = m*scale
λ = scale

To go the other way:

m     = μ/λ
loc   = 0
scale = λ

[1]

“Inverse Gaussian distribution”, Wikipedia, https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution

mpsci.distributions.invgauss.cdf(x, m, loc=0, scale=1)

CDF for the inverse Gaussian distribution.

mpsci.distributions.invgauss.entropy(m, loc=0, scale=1)

Differential entropy of the inverse Gaussian distribution.

mpsci.distributions.invgauss.invcdf(p, m, loc=0, scale=1)

Inverse of the CDF for the inverse Gaussian distribution.

mpsci.distributions.invgauss.invsf(p, m, loc=0, scale=1)

Inverse of the survival function for the inverse Gaussian distribution.

mpsci.distributions.invgauss.logcdf(x, m, loc=0, scale=1)

Logarithm of the CDF for the inverse Gaussian distribution.

mpsci.distributions.invgauss.logpdf(x, m, loc=0, scale=1)

Logarithm of the PDF for the inverse Gaussian distribution.

mpsci.distributions.invgauss.logsf(x, m, loc=0, scale=1)

Logarithm of the survival function for the inverse Gaussian distribution.

mpsci.distributions.invgauss.mean(m, loc=0, scale=1)

Mean of the inverse Gaussian distribution.

mpsci.distributions.invgauss.median(m, loc=0, scale=1)

Median of the inverse Gaussian distribution.

mpsci.distributions.invgauss.mode(m, loc=0, scale=1)

Mode of the inverse Gaussian distribution.

mpsci.distributions.invgauss.noncentral_moment(n, m, loc=0, scale=1)

Noncentral moment of the generalized extreme value distribution.

The value is also known as the raw moment.

mpsci.distributions.invgauss.pdf(x, m, loc=0, scale=1)

PDF for the inverse Gaussian distribution.

mpsci.distributions.invgauss.sf(x, m, loc=0, scale=1)

Survival function for the inverse Gaussian distribution.

mpsci.distributions.invgauss.support(m, loc=0, scale=1)

Support of the inverse Gaussian distribution.

mpsci.distributions.invgauss.var(m, loc=0, scale=1)

Variance of the inverse Gaussian distribution.