Random Matrix Statistics
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Under Construction! Current version posted: August 18, 2005. You need the
mhg package for the functions here to work.
Installation instructions:
Download and unzip the package rms.zip.
Other resources
- Ioana Dumitriu's MOPs
package for computing with Multivariate Orthogonal Polynomials.
Function description:
mhg, mhgi, logmhg
| Description: |
Computes the Hypergeometric function of one or
two matrix arguments. See here for
details.
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gammam
| Syntax: |
y=gammam(beta,m,a) |
| Description: |
Computes the multivariate Gamma function of parameter beta.
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| Comments: |
beta=2/alpha.
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pdfTraceWishart
| Syntax: |
f=pdfTraceWishart(MAX,u,Sigma,m) |
| Description: |
Computes the pdf of the tr(A), where A is an m-by-n Wishart matrix
with m degrees of freedom and covariance matrix Sigma.
|
| Comments: |
- See Muirhead, 1978, p. 341 for theoretical background.
- u is a vector, e.g., u=[0:0.1:30]; the function returns f(u),
where f is the pdf of tr(A)
- Although in practice Sigma is a matrix, only its eigenvalues factor in
the computation, so the parameter Sigma is simply a vector of its
eigenvalues.
- A large enough
value of MAX should be supplied to guarantee convergence of the series.
- Run pdfTraceWishartTEST to see an example.
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pdfTraceWishartTEST
| Syntax: |
pdfTraceWishartTEST |
| Description: |
A script for testing pdfTraceWishart against the results of a
Monte-Carlo experiment. |
| Comments: |
Enter your own values for
m, Sigma, and MAX. MAX must be large enough to guarantee
convergence of the underlying series.
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pdfMinEigBetaLaguerre
| Syntax: |
f=pdfMinEigBetaLaguerre(M,beta,n,a,x) |
| Description: |
returns the pdf of the smallest eigenvalue of an n-by-n
beta-Laguerre matrix of parameter a.
|
| Arguments: |
- M is an integer, indicates the depth of the truncation, larger
values will yield more accurate result, but will also take more time.
- beta is positive and equals 2/alpha
- n is the size of the matrix
- a is a parameter, we must have a>beta*(n-1)/2
- x is a set of values on which the pdf is to be evaluated
|
| Comments: |
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pdfMinEigBetaLaguerreTEST
| Syntax: |
pdfMinEigBetaLaguerreTEST |
| Description: |
A script for testing pdfMinEigBetaLaguerre against the
result of a Monte-Carlo experiment.
|
cdfMaxEigWishart
| Syntax: |
f=cdfMaxEigWishart(MAX) |
| Description: |
Computes the cumulative distribution function of the largest
eigenvalue of an n-by-n Wishart matrix with k degrees of freedom and
covariance matrix Sigma.
|
| Comments: |
Enter your own values for
m, Sigma, and MAX. MAX must be large enough to guarantee
convergence of the underlying series.
|
cdfMaxEigWishartTEST
| Syntax: |
cdfMaxEigWishartTEST |
| Description: |
A script for testing cdfMaxEigWishart against the results of a
Monte-Carlo experiment. |
| Comments: |
Enter your own values for
m, Sigma, and MAX. MAX must be large enough to guarantee
convergence of the underlying series.
|
cdfMaxEigBetaLaguerre
| Syntax: |
f=cdfMaxEigBetaLaguerre() |
| Description: |
Comutes the CDF of the largest eigenvalue of an n-by-n
Beta-Laguerre matrix of parameter a.
|
| Comments: |
Enter your own values for
m, Sigma, and MAX. MAX must be large enough to guarantee
convergence of the underlying series.
|
cdfMaxEigBetaLaguerreTEST
| Syntax: |
cdfMaxEigBetaLaguerreTEST |
| Description: |
A script for testing cdfMaxEigBetaLaguerre against the results of
a Monte-Carlo experiment.
|
| Comments: |
Enter your own values for
m, Sigma, and MAX. MAX must be large enough to guarantee
convergence of the underlying series.
|
Plamen Koev
Department of Mathematics, Massachusetts Institute
of Technology
"firstname"@math.mit.edu
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