randomgen.generator.ExtendedGenerator.standard_wishart¶
- ExtendedGenerator.standard_wishart(df, dim, size=None)¶
Draw samples from the Standard Wishart and Pseudo-Wishart distributions
- Parameters:
- dfint
The degree-of-freedom for the simulated Wishart variates.
- dimint
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)
, thenm * 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).
- Returns:
- ndarray
The generated variates from the standard wishart distribution.
See also
wishart
Generate variates with a non-identify scale. Also support array inputs for df.
Notes
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.
References
[1]Odell, P. L. , and A. H. Feiveson (1966) A numerical procedure to generate a sample covariance matrix. Jour. Amer. Stat. Assoc. 61, 199–203
[2]Uhlig, H. (1994). “On Singular Wishart and Singular Multivariate Beta Distributions”. The Annals of Statistics. 22: 395–405
[3]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.