mvem.stats.multivariate_t

mvem.stats.multivariate_t.fit

mvem.stats.multivariate_t.fit(X, maxiter=100, ptol=1e-06, ftol=1e-08, return_loglike=False)[source]

Fit the parameters of the multivariate Student’s t-distribution to data using an EM algorithm. We use the location-scale parameterisation.

Parameters

X (np.ndarray) – An array of shape (n, p) containing n observations of some p-variate data with n > p.
maxiter – The maximum number of iterations to use in the EM algorithm. Defaults to 100.
ptol (float, optional) – The relative convergence criterion for the estimated parameters. Defaults to 1e-6.
ftol (float, optional) – The relative convergence criterion for the log-likelihood function. Defaults to np.inf.
return_loglike (np.ndarray, optional) – Return a list of log-likelihood values at each iteration. Defaults to False.

Returns

The fitted parameters (<array> mu, <array> scale, <float> df). Also returns a list of log-likelihood values at each iteration of the EM algorithm if return_loglike=True.

Return type

tuple

mvem.stats.multivariate_t.loglike

mvem.stats.multivariate_t.loglike(x, loc, shape, df, allow_singular=False)[source]

Log-likelihood function of the multivariate Student’s t-distribution. We use the location-scale parameterisation.

Parameters

x (np.ndarray) – An array of shape (n, p) containing n observations of some p-variate data with n > p.
loc (np.ndarray) – The location parameter with shape (p,).
shape (np.ndarray) – The shape parameter. A positive semi-definite array with shape (p, p).
df (float) – The degrees of freedom of the distribution, > 0.
allow_singular (bool, optional.) – Whether to allow a singular matrix.

Returns

The log-likelihood for given all observations and parameters.

Return type

float

mvem.stats.multivariate_t.logpdf

mvem.stats.multivariate_t.logpdf(x, loc, shape, df, allow_singular=False)[source]

Log-probability density function of the multivariate Student’s t-distribution. We use the location-scale parameterisation.

Parameters

x (np.ndarray) – An array of shape (n, p) containing n observations of some p-variate data with n > p.
loc (np.ndarray) – The location parameter with shape (p,).
shape (np.ndarray) – The shape parameter. A positive semi-definite array with shape (p, p).
df (float) – The degrees of freedom of the distribution, > 0.
allow_singular (bool, optional.) – Whether to allow a singular matrix.

Returns

The log-density at each observation.

Return type

np.ndarray with shape (p,).

mvem.stats.multivariate_t.mean

mvem.stats.multivariate_t.mean(loc, shape, df)[source]

Mean of the multivariate Student’s t-distribution. We use the location-scale parameterisation.

Parameters

loc (np.ndarray) – The location parameter with shape (p,).
shape (np.ndarray) – The shape parameter. A positive semi-definite array with shape (p, p).
df (float) – The degrees of freedom of the distribution, > 0.

Returns

The mean of the specified distribution.

Return type

np.ndarray with shape (p,).

mvem.stats.multivariate_t.pdf

mvem.stats.multivariate_t.pdf(x, loc, shape, df, allow_singular=False)[source]

Probability density function of the multivariate Student’s t-distribution. We use the location-scale parameterisation.

Parameters

x (np.ndarray) – An array of shape (n, p) containing n observations of some p-variate data with n > p.
loc (np.ndarray) – The location parameter with shape (p,).
shape (np.ndarray) – The shape parameter. A positive semi-definite array with shape (p, p).
df (float) – The degrees of freedom of the distribution, > 0.
allow_singular (bool, optional.) – Whether to allow a singular matrix.

Returns

The density at each observation.

Return type

np.ndarray with shape (p,).

mvem.stats.multivariate_t.rvs

mvem.stats.multivariate_t.rvs(loc, shape, df, size=1, random_state=None)[source]

Random number generator of the multivariate Student’s t-distribution. We use the location-scale parameterisation.

Parameters

loc (np.ndarray) – The location parameter with shape (p,).
shape (np.ndarray) – The shape parameter. A positive semi-definite array with shape (p, p).
df (float) – The degrees of freedom of the distribution, > 0.
size (int, optional) – The number of samples to draw. Defaults to 1.
random_state (None, int, np.random.RandomState, np.random.Generator, optional) – Used for drawing random variates. Defaults to None.

Returns

The random p-variate numbers generated.

Return type

np.ndarray with shape (n, p).

mvem.stats.multivariate_t.var

mvem.stats.multivariate_t.var(loc, shape, df)[source]

Variance of the multivariate Student’s t-distribution. We use the location-scale parameterisation.

Parameters

loc (np.ndarray) – The location parameter with shape (p,).
shape (np.ndarray) – The shape parameter. A positive semi-definite array with shape (p, p).
df (float) – The degrees of freedom of the distribution, > 0.

Returns

The variance of the specified distribution.

Return type

np.ndarray with shape (p,).