scipy.stats.multivariate_t#
- scipy.stats.multivariate_t = <scipy.stats._multivariate.multivariate_t_gen object>[source]#
- A multivariate t-distributed random variable. - The loc parameter specifies the location. The shape parameter specifies the positive semidefinite shape matrix. The df parameter specifies the degrees of freedom. - In addition to calling the methods below, the object itself may be called as a function to fix the location, shape matrix, and degrees of freedom parameters, returning a “frozen” multivariate t-distribution random. - Parameters:
- locarray_like, optional
- Location of the distribution. (default - 0)
- shapearray_like, optional
- Positive semidefinite matrix of the distribution. (default - 1)
- dffloat, optional
- Degrees of freedom of the distribution; must be greater than zero. If - np.infthen results are multivariate normal. The default is- 1.
- allow_singularbool, optional
- Whether to allow a singular matrix. (default - False)
- seed{None, int, np.random.RandomState, np.random.Generator}, optional
- Used for drawing random variates. If seed is None, the RandomState singleton is used. If seed is an int, a new - RandomStateinstance is used, seeded with seed. If seed is already a- RandomStateor- Generatorinstance, then that object is used. Default is None.
 
 - Notes - Setting the parameter loc to - Noneis equivalent to having loc be the zero-vector. The parameter shape can be a scalar, in which case the shape matrix is the identity times that value, a vector of diagonal entries for the shape matrix, or a two-dimensional array_like. The matrix shape must be a (symmetric) positive semidefinite matrix. The determinant and inverse of shape are computed as the pseudo-determinant and pseudo-inverse, respectively, so that shape does not need to have full rank.- The probability density function for - multivariate_tis\[f(x) = \frac{\Gamma((\nu + p)/2)}{\Gamma(\nu/2)\nu^{p/2}\pi^{p/2}|\Sigma|^{1/2}} \left[1 + \frac{1}{\nu} (\mathbf{x} - \boldsymbol{\mu})^{\top} \boldsymbol{\Sigma}^{-1} (\mathbf{x} - \boldsymbol{\mu}) \right]^{-(\nu + p)/2},\]- where \(p\) is the dimension of \(\mathbf{x}\), \(\boldsymbol{\mu}\) is the \(p\)-dimensional location, \(\boldsymbol{\Sigma}\) the \(p \times p\)-dimensional shape matrix, and \(\nu\) is the degrees of freedom. - Added in version 1.6.0. - References [1]- Arellano-Valle et al. “Shannon Entropy and Mutual Information for Multivariate Skew-Elliptical Distributions”. Scandinavian Journal of Statistics. Vol. 40, issue 1. - Examples - The object may be called (as a function) to fix the loc, shape, df, and allow_singular parameters, returning a “frozen” multivariate_t random variable: - >>> import numpy as np >>> from scipy.stats import multivariate_t >>> rv = multivariate_t([1.0, -0.5], [[2.1, 0.3], [0.3, 1.5]], df=2) >>> # Frozen object with the same methods but holding the given location, >>> # scale, and degrees of freedom fixed. - Create a contour plot of the PDF. - >>> import matplotlib.pyplot as plt >>> x, y = np.mgrid[-1:3:.01, -2:1.5:.01] >>> pos = np.dstack((x, y)) >>> fig, ax = plt.subplots(1, 1) >>> ax.set_aspect('equal') >>> plt.contourf(x, y, rv.pdf(pos))   - Methods - pdf(x, loc=None, shape=1, df=1, allow_singular=False) - Probability density function. - logpdf(x, loc=None, shape=1, df=1, allow_singular=False) - Log of the probability density function. - cdf(x, loc=None, shape=1, df=1, allow_singular=False, *, - maxpts=None, lower_limit=None, random_state=None) Cumulative distribution function. - rvs(loc=None, shape=1, df=1, size=1, random_state=None) - Draw random samples from a multivariate t-distribution. - entropy(loc=None, shape=1, df=1) - Differential entropy of a multivariate t-distribution.