mvem.stats.gig
mvem.stats.gig.cdf
- mvem.stats.gig.cdf(x, lmbda=1, chi=1, psi=1)[source]
Cumulative density function of the GIG distribution.
- Parameters
x (np.ndarray) – An array of shape (n,) containing n observations of some univariate data.
lmbda (float) – Univariate parameter.
chi (float) – Univariate parameter.
psi (float) – Univariate parameter.
- Returns
The cumulative density at each observation.
- Return type
np.ndarray with shape (n,).
mvem.stats.gig.expect
- mvem.stats.gig.expect(lmbda, chi, psi, func='x')[source]
Compute the expectation E[f(x)|lmbda, chi, psi], where f(x) is one of [“x”, “logx”, “1/x”].
- Parameters
lmbda (float) – Univariate parameter.
chi (float) – Univariate parameter.
psi (float) – Univariate parameter.
func (str, optional) – The function to compute the expectation of. One of [“x”, “logx”, “1/x”]. Default to “x”.
- Returns
The expected value
- Return type
float
mvem.stats.gig.logcdf
- mvem.stats.gig.logcdf(x, lmbda=1, chi=1, psi=1)[source]
Log-cumulative density function of the GIG distribution.
- Parameters
x (np.ndarray) – An array of shape (n,) containing n observations of some univariate data.
lmbda (float) – Univariate parameter.
chi (float) – Univariate parameter.
psi (float) – Univariate parameter.
- Returns
The log-cumulative density at each observation.
- Return type
np.ndarray with shape (n,).
mvem.stats.gig.logpdf
- mvem.stats.gig.logpdf(x, lmbda=1, chi=1, psi=1)[source]
Log-probability density function of the GIG distribution.
- Parameters
x (np.ndarray) – An array of shape (n,) containing n observations of some univariate data.
lmbda (float) – Univariate parameter.
chi (float) – Univariate parameter.
psi (float) – Univariate parameter.
- Returns
The log-density at each observation.
- Return type
np.ndarray with shape (n,).
mvem.stats.gig.pdf
- mvem.stats.gig.pdf(x, lmbda=1, chi=1, psi=1)[source]
Probability density function of the GIG distribution.
- Parameters
x (np.ndarray) – An array of shape (n,) containing n observations of some univariate data.
lmbda (float) – Univariate parameter.
chi (float) – Univariate parameter.
psi (float) – Univariate parameter.
- Returns
The density at each observation.
- Return type
np.ndarray with shape (n,).
mvem.stats.gig.rvs
- mvem.stats.gig.rvs(lmbda=1, chi=1, psi=1, size=1)[source]
Random number generator of the GIG distribution.
- Parameters
lmbda (float) – Univariate parameter.
chi (float) – Univariate parameter.
psi (float) – Univariate parameter.
size (int, optional) – The number of samples to draw. Defaults to 1.
- Returns
The random univariate numbers generated.
- Return type
np.ndarray with shape (n,).
mvem.stats.gig.var
- mvem.stats.gig.var(lmbda, chi, psi)[source]
Compute the variance of a GIG distribution with parameters (lmbda, chi, psi). When psi==0, the distribution is the inverse Gamma distribution, and when chi==0, the distribution is the Gamma distribution.
Handles a vector of parameters, if the different distributions all belong to the same group. That is, if chi==0 for one set of parameters, it must be so for all sets of parameters.
- Parameters
lmbda (float) – Univariate parameter.
chi (float) – Univariate parameter.
psi (float) – Univariate parameter.
- Returns
The variance
- Return type
float