ExtendedGenerator.standard_wishart(df, dim, size=None)

Draw samples from the Standard Wishart and Pseudo-Wishart distributions


The degree-of-freedom for the simulated Wishart variates.


The dimension of the simulated Wishart variates.

sizeint or tuple of ints, optional

Output shape, excluding trailing dims. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn, each with shape (dim, dim). The output then has shape (m, n, k, dim, dim). Default is None, in which case a single value with shape (dim, dim) is returned.

rescalebool, optional

Flag indicating whether to rescale the outputs to have expectation identity. The default is True. If rescale is False, then the expected value of the generated variates is df * eye(dim).


The generated variates from the standard wishart distribution.

See also


Generate variates with a non-identify scale. Also support array inputs for df.


Uses the method of Odell and Feiveson [1] when df >= dim. Otherwise variates are directly generated as the inner product of df by dim arrays of standard normal random variates.



Odell, P. L. , and A. H. Feiveson (1966) A numerical procedure to generate a sample covariance matrix. Jour. Amer. Stat. Assoc. 61, 199–203


Uhlig, H. (1994). “On Singular Wishart and Singular Multivariate Beta Distributions”. The Annals of Statistics. 22: 395–405


Dıaz-Garcıa, J. A., Jáimez, R. G., & Mardia, K. V. (1997). Wishart and Pseudo-Wishart distributions and some applications to shape theory. Journal of Multivariate Analysis, 63(1), 73-87.