scipy.stats.invgauss¶
-
scipy.stats.
invgauss
= <scipy.stats._continuous_distns.invgauss_gen object>[source]¶ An inverse Gaussian continuous random variable.
As an instance of the
rv_continuous
class,invgauss
object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.Notes
The probability density function for
invgauss
is:\[f(x, \mu) = \frac{1}{\sqrt{2 \pi x^3}} \exp(-\frac{(x-\mu)^2}{2 x \mu^2})\]for \(x > 0\).
invgauss
takes \(\mu\) as a shape parameter.The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the
loc
andscale
parameters. Specifically,invgauss.pdf(x, mu, loc, scale)
is identically equivalent toinvgauss.pdf(y, mu) / scale
withy = (x - loc) / scale
.When \(\mu\) is too small, evaluating the cumulative distribution function will be inaccurate due to
cdf(mu -> 0) = inf * 0
. NaNs are returned for \(\mu \le 0.0028\).Examples
>>> from scipy.stats import invgauss >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate a few first moments:
>>> mu = 0.145 >>> mean, var, skew, kurt = invgauss.stats(mu, moments='mvsk')
Display the probability density function (
pdf
):>>> x = np.linspace(invgauss.ppf(0.01, mu), ... invgauss.ppf(0.99, mu), 100) >>> ax.plot(x, invgauss.pdf(x, mu), ... 'r-', lw=5, alpha=0.6, label='invgauss pdf')
Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a “frozen” RV object holding the given parameters fixed.
Freeze the distribution and display the frozen
pdf
:>>> rv = invgauss(mu) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of
cdf
andppf
:>>> vals = invgauss.ppf([0.001, 0.5, 0.999], mu) >>> np.allclose([0.001, 0.5, 0.999], invgauss.cdf(vals, mu)) True
Generate random numbers:
>>> r = invgauss.rvs(mu, size=1000)
And compare the histogram:
>>> ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2) >>> ax.legend(loc='best', frameon=False) >>> plt.show()
Methods
rvs(mu, loc=0, scale=1, size=1, random_state=None)
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 distribution function. logcdf(x, mu, loc=0, scale=1)
Log of the cumulative distribution function. sf(x, mu, loc=0, scale=1)
Survival function (also defined as 1 - cdf
, but sf is 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, args=(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