scipy.stats.multivariate_normal#
- scipy.stats.multivariate_normal = <scipy.stats._multivariate.multivariate_normal_gen object>[source]#
- A multivariate normal random variable. - The mean keyword specifies the mean. The cov keyword specifies the covariance matrix. - Parameters:
- meanarray_like, default: [0]
- Mean of the distribution. 
- covarray_like or Covariance, default:[1]
- Symmetric positive (semi)definite covariance matrix of the distribution. 
- allow_singularbool, default: False
- Whether to allow a singular covariance matrix. This is ignored if cov is a - Covarianceobject.
- 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.
 
- meanarray_like, default: 
 - Methods - pdf(x, mean=None, cov=1, allow_singular=False) - Probability density function. - logpdf(x, mean=None, cov=1, allow_singular=False) - Log of the probability density function. - cdf(x, mean=None, cov=1, allow_singular=False, maxpts=1000000*dim, abseps=1e-5, releps=1e-5, lower_limit=None) - Cumulative distribution function. - logcdf(x, mean=None, cov=1, allow_singular=False, maxpts=1000000*dim, abseps=1e-5, releps=1e-5) - Log of the cumulative distribution function. - rvs(mean=None, cov=1, size=1, random_state=None) - Draw random samples from a multivariate normal distribution. - entropy(mean=None, cov=1) - Compute the differential entropy of the multivariate normal. - fit(x, fix_mean=None, fix_cov=None) - Fit a multivariate normal distribution to data. - 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, a two-dimensional array_like, or a - Covarianceobject.- The covariance matrix cov may be an instance of a subclass of - Covariance, e.g. scipy.stats.CovViaPrecision. If so, allow_singular is ignored.- Otherwise, cov must be a symmetric positive semidefinite matrix when allow_singular is True; it must be (strictly) positive definite when allow_singular is False. Symmetry is not checked; only the lower triangular portion is used. 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_normalis\[f(x) = \frac{1}{\sqrt{(2 \pi)^k \det \Sigma}} \exp\left( -\frac{1}{2} (x - \mu)^T \Sigma^{-1} (x - \mu) \right),\]- where \(\mu\) is the mean, \(\Sigma\) the covariance matrix, \(k\) the rank of \(\Sigma\). In case of singular \(\Sigma\), SciPy extends this definition according to [1]. - Added in version 0.14.0. - References [1]- Multivariate Normal Distribution - Degenerate Case, Wikipedia, https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Degenerate_case - Examples - >>> import numpy as np >>> import matplotlib.pyplot as plt >>> 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]) >>> fig1 = plt.figure() >>> ax = fig1.add_subplot(111) >>> ax.plot(x, y) >>> plt.show()   - 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, cov=1, allow_singular=False) >>> # Frozen object with the same methods but holding the given >>> # mean and covariance fixed. - 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.dstack((x, y)) >>> rv = multivariate_normal([0.5, -0.2], [[2.0, 0.3], [0.3, 0.5]]) >>> fig2 = plt.figure() >>> ax2 = fig2.add_subplot(111) >>> ax2.contourf(x, y, rv.pdf(pos)) 