Density, distribution function, quantile function, and random
generation for the Tracy-Widom distribution with order parameter
beta.
dtw(x, beta=1, log = FALSE)
ptw(q, beta=1, lower.tail = TRUE, log.p = FALSE)
qtw(p, beta=1, lower.tail = TRUE, log.p = FALSE)
rtw(n, beta=1)vector of quantiles.
vector of probabilities.
number of observations. If length(n) > 1, the length
is taken to be the number required.
the order parameter (1, 2, or 4).
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).
dtw gives the density,
ptw gives the distribution function,
qtw gives the quantile function, and
rtw generates random deviates.
If beta is not specified, it assumes the default value of 1.
The Tracy-Widom law is the edge-scaled limiting distribution of the
largest eigenvalue of a random matrix from the \(\beta\)-ensemble.
Supported values for beta are 1 (Gaussian Orthogonal Ensemble),
2 (Gaussian Unitary Ensemble), and 4 (Gaussian Symplectic
Ensemble).
Dieng, M. (2006). Distribution functions for edge eigenvalues in orthogonal and symplectic ensembles: Painlev<U+00E9> representations. arXiv:math/0506586v2 [math.PR].
Tracy, C.A. and Widom, H. (1994). Level-spacing distributions and the Airy kernel. Communications in Mathematical Physics 159, 151--174.
Tracy, C.A. and Widom, H. (1996). On orthogonal and symplectic matrix ensembles. Communications in Mathematical Phsyics 177, 727--754.