mvem.stats.multivariate_skewnorm
mvem.stats.multivariate_skewnorm.fit
- mvem.stats.multivariate_skewnorm.fit(x, maxiter=100, ptol=1e-06, ftol=inf, eps=0.9, return_loglike=False)[source]
Estimate the parameters of the multivariate skew normal distribution using an EM algorithm.
- 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.
eps (float, optional) – Initialization shrinkage of delta parameter. Defaults to 0.9.
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, <array> nu). 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_skewnorm.loglike
- mvem.stats.multivariate_skewnorm.loglike(x, mu, sigma, lmbda)[source]
Log-likelihood function of the multivariate skew normal distribution.
- Parameters
x (np.ndarray) – An array of shape (n, p) containing n observations of some p-variate data with n > p.
mu (np.ndarray) – The location parameter with shape (p,).
sigma (np.ndarray) – The scale parameter. A positive semi-definite array with shape (p, p).
lmbda (np.ndarray) – The skewness parameter with shape (p,).
- Returns
The log-likelihood for given all observations and parameters.
- Return type
float
mvem.stats.multivariate_skewnorm.logpdf
- mvem.stats.multivariate_skewnorm.logpdf(x, mu, sigma, lmbda)[source]
Log-probability density function of the multivariate skew normal distribution.
- Parameters
x (np.ndarray) – An array of shape (n, p) containing n observations of some p-variate data with n > p.
mu (np.ndarray) – The location parameter with shape (p,).
sigma (np.ndarray) – The scale parameter. A positive semi-definite array with shape (p, p).
lmbda (np.ndarray) – The skewness parameter with shape (p,).
- Returns
The log-density at each observation.
- Return type
np.ndarray with shape (p,).
mvem.stats.multivariate_skewnorm.mean
- mvem.stats.multivariate_skewnorm.mean(mu, sigma, lmbda)[source]
Mean function of the multivariate skew normal distribution.
- Parameters
mu (np.ndarray) – The location parameter with shape (p,).
sigma (np.ndarray) – The scale parameter. A positive semi-definite array with shape (p, p).
lmbda (np.ndarray) – The skewness parameter with shape (p,).
- Returns
The mean of the specified distribution.
- Return type
np.ndarray with shape (p,).
mvem.stats.multivariate_skewnorm.pdf
- mvem.stats.multivariate_skewnorm.pdf(x, mu, sigma, lmbda)[source]
Probability density function of the multivariate skew normal distribution.
- Parameters
x (np.ndarray) – An array of shape (n, p) containing n observations of some p-variate data with n > p.
mu (np.ndarray) – The location parameter with shape (p,).
sigma (np.ndarray) – The scale parameter. A positive semi-definite array with shape (p, p).
lmbda (np.ndarray) – The skewness parameter with shape (p,).
- Returns
The density at each observation.
- Return type
np.ndarray with shape (p,).
mvem.stats.multivariate_skewnorm.rvs
- mvem.stats.multivariate_skewnorm.rvs(mu, sigma, lmbda, size=1)[source]
Random number generator of the multivariate skew normal distribution.
- Parameters
mu (np.ndarray) – The location parameter with shape (p,).
sigma (np.ndarray) – The scale parameter. A positive semi-definite array with shape (p, p).
lmbda (np.ndarray) – The skewness parameter with shape (p,).
size (int, optional) – The number of samples to draw. Defaults to 1.
- Returns
The random p-variate numbers generated.
- Return type
np.ndarray with shape (n, p).
mvem.stats.multivariate_skewnorm.var
- mvem.stats.multivariate_skewnorm.var(mu, sigma, lmbda)[source]
Variance function of the multivariate skew normal distribution.
- Parameters
mu (np.ndarray) – The location parameter with shape (p,).
sigma (np.ndarray) – The scale parameter. A positive semi-definite array with shape (p, p).
lmbda (np.ndarray) – The skewness parameter with shape (p,).
- Returns
The variance of the specified distribution.
- Return type
np.ndarray with shape (p,).