scipy.stats.multivariate_normal¶
- scipy.stats.multivariate_normal = <scipy.stats._multivariate.multivariate_normal_gen object at 0x2b45d3298990>[source]¶
A multivariate normal random variable.
The mean keyword specifies the mean. The cov keyword specifies the covariance matrix.
New in version 0.14.0.
Parameters: x : array_like
Quantiles, with the last axis of x denoting the components.
mean : array_like, optional
Mean of the distribution (default zero)
cov : array_like, optional
Covariance matrix of the distribution (default one)
Alternatively, the object may be called (as a function) to fix the mean
and covariance parameters, returning a “frozen” multivariate normal
random variable:
rv = multivariate_normal(mean=None, scale=1)
- Frozen object with the same methods but holding the given mean and covariance fixed.
Notes
Setting the parameter mean to None is equivalent to having mean be the zero-vector. The parameter cov can be a scalar, in which case the covariance matrix is the identity times that value, a vector of diagonal entries for the covariance matrix, or a two-dimensional array_like.
The covariance matrix cov must be a (symmetric) positive semi-definite matrix. The determinant and inverse of cov are computed as the pseudo-determinant and pseudo-inverse, respectively, so that cov does not need to have full rank.
The probability density function for multivariate_normal is
where
is the mean,
the covariance matrix, and
is the dimension of the space where
takes values.
Examples
>>> from scipy.stats import multivariate_normal >>> x = np.linspace(0, 5, 10, endpoint=False) >>> y = multivariate_normal.pdf(x, mean=2.5, cov=0.5); y array([ 0.00108914, 0.01033349, 0.05946514, 0.20755375, 0.43939129, 0.56418958, 0.43939129, 0.20755375, 0.05946514, 0.01033349]) >>> plt.plot(x, y)
The input quantiles can be any shape of array, as long as the last axis labels the components. This allows us for instance to display the frozen pdf for a non-isotropic random variable in 2D as follows:
>>> x, y = np.mgrid[-1:1:.01, -1:1:.01] >>> pos = np.empty(x.shape + (2,)) >>> pos[:, :, 0] = x; pos[:, :, 1] = y >>> rv = multivariate_normal([0.5, -0.2], [[2.0, 0.3], [0.3, 0.5]]) >>> plt.contourf(x, y, rv.pdf(pos))
Methods
pdf(x, mean=None, cov=1) Probability density function. logpdf(x, mean=None, cov=1) Log of the probability density function. rvs(mean=None, cov=1) Draw random samples from a multivariate normal distribution. entropy() Compute the differential entropy of the multivariate normal.