scipy.stats.invgauss = <scipy.stats.distributions.invgauss_gen object at 0x44f11d0>[source]

An inverse Gaussian continuous random variable.

Continuous random variables are defined from a standard form and may require some shape parameters to complete its specification. Any optional keyword parameters can be passed to the methods of the RV object as given below:

Parameters :

x : array_like


q : array_like

lower or upper tail probability

mu : array_like

shape parameters

loc : array_like, optional

location parameter (default=0)

scale : array_like, optional

scale parameter (default=1)

size : int or tuple of ints, optional

shape of random variates (default computed from input arguments )

moments : str, optional

composed of letters [‘mvsk’] specifying which moments to compute where ‘m’ = mean, ‘v’ = variance, ‘s’ = (Fisher’s) skew and ‘k’ = (Fisher’s) kurtosis. (default=’mv’)

Alternatively, the object may be called (as a function) to fix the shape, :

location, and scale parameters returning a “frozen” continuous RV object: :

rv = invgauss(mu, loc=0, scale=1) :

  • Frozen RV object with the same methods but holding the given shape, location, and scale fixed.


The probability density function for invgauss is:

invgauss.pdf(x, mu) = 1 / sqrt(2*pi*x**3) * exp(-(x-mu)**2/(2*x*mu**2))

for x > 0.

When mu is too small, evaluating the cumulative density function will be inaccurate due to cdf(mu -> 0) = inf * 0. NaNs are returned for mu <= 0.0028.


>>> from scipy.stats import invgauss
>>> numargs = invgauss.numargs
>>> [ mu ] = [0.9,] * numargs
>>> rv = invgauss(mu)

Display frozen pdf

>>> x = np.linspace(0, np.minimum(rv.dist.b, 3))
>>> h = plt.plot(x, rv.pdf(x))

Here, rv.dist.b is the right endpoint of the support of rv.dist.

Check accuracy of cdf and ppf

>>> prb = invgauss.cdf(x, mu)
>>> h = plt.semilogy(np.abs(x - invgauss.ppf(prb, mu)) + 1e-20)

Random number generation

>>> R = invgauss.rvs(mu, size=100)


rvs(mu, loc=0, scale=1, size=1) Random variates.
pdf(x, mu, loc=0, scale=1) Probability density function.
logpdf(x, mu, loc=0, scale=1) Log of the probability density function.
cdf(x, mu, loc=0, scale=1) Cumulative density function.
logcdf(x, mu, loc=0, scale=1) Log of the cumulative density function.
sf(x, mu, loc=0, scale=1) Survival function (1-cdf — sometimes more accurate).
logsf(x, mu, loc=0, scale=1) Log of the survival function.
ppf(q, mu, loc=0, scale=1) Percent point function (inverse of cdf — percentiles).
isf(q, mu, loc=0, scale=1) Inverse survival function (inverse of sf).
moment(n, mu, loc=0, scale=1) Non-central moment of order n
stats(mu, loc=0, scale=1, moments=’mv’) Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(mu, loc=0, scale=1) (Differential) entropy of the RV.
fit(data, mu, loc=0, scale=1) Parameter estimates for generic data.
expect(func, mu, loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds) Expected value of a function (of one argument) with respect to the distribution.
median(mu, loc=0, scale=1) Median of the distribution.
mean(mu, loc=0, scale=1) Mean of the distribution.
var(mu, loc=0, scale=1) Variance of the distribution.
std(mu, loc=0, scale=1) Standard deviation of the distribution.
interval(alpha, mu, loc=0, scale=1) Endpoints of the range that contains alpha percent of the distribution

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