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
mean : array_like, optional
cov : array_like, optional
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)
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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. |