pydygp.probabilitydistributions.InverseGamma

class pydygp.probabilitydistributions.InverseGamma(a=1, b=1)

__init__(a=1, b=1)

Inverse Gamma probability distribution

Notes

The probability density for the Inverse Gamma distribution is

\[p(x) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} x^{-(\alpha+1)} e^{-\beta x^{-1}}\]

where \(\alpha\) is the shape parameter and \(\beta\) is the scale parameter.

Examples

>>> # compare with the gamma distribution in scipy.stats
>>> from scipy.stats import gamma
>>> p = InverseGamma()
>>> q = p.logtransform()  # dist. of log transformed inv. gamma r.v.
>>> z = gamma.rvs(a=2, size=1000)
>>> x = np.linspace(-5., 5., 100)
>>> # plot the pdf of the log transformed inv. gamma r.v.
>>> plt.plot(x, np.exp(q.logpdf(x)))
>>> # plot the histogram of log(1/Z) Z ~ gamma(a, b)
>>> plt.hist(-np.log(z), density=True, alpha=0.5)

(Source code, png, hires.png, pdf)

logtransform()

Distribution of the log-transformed random variable.

Returns:

prob_dist : ProbabilityDistribution

The distribution of the log-transformed random variable represented as a UnivariateProbabilityDistribution object.