Probability density function:

Cumulative distribution function:

Mean and variance:

Median:

Generate a sample of pseudorandom numbers from a Tracy–Widom distribution:

Compare its histogram to the PDF:

Moments of Tracy–Widom distributions are not available in closed form:

Find their machine‐precision approximation:

Compute the Mean of Tracy–Widom distribution to 50‐digit precision:

Hazard function:

Quantile function:

Use MatrixPropertyDistribution to represent the normalized largest eigenvalue of a matrix from Gaussian unitary ensemble:

Sample from MatrixPropertyDistribution:

Compare the histogram with the PDF:

Perform similar computations with Gaussian orthogonal ensemble and Gaussian symplectic ensemble:

Compare the histograms with the PDFs:

When n and p (the dimension of the covariance matrix Σ) are both large, the scaled largest eigenvalue of a matrix from Wishart ensemble with identity covariance is approximately distributed as Tracy–Widom distribution of :

Sample the scaled largest eigenvalue:

Compare the histogram of scaled largest eigenvalues with the PDF:

Compare the CDFs of Tracy–Widom distributions with the leading order asymptotic expansion on the left tail in log scale:

Define a function to find the length of LongestOrderedSequence in the given sequence:

Find lengths of the longest increasing subsequence in random permutations of list :

Compare the scaled length of the longest increasing subsequence with Tracy–Widom distribution of :

CDFs of Tracy–Widom distributions for different values of β are related to each other:

Tracy–Widom distributions can be well approximated by GammaDistribution in the central region:

Match GammaDistribution with Tracy–Widom distribution of with the first three moments:

Compare the PDFs between :

Compare the CDFs between in log scale: