The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution supported on the interval the graph of whose probability density function f is a semicircle of radius R centered at (0, 0) and then suitably normalized (so that it is really a semi-ellipse):
for −R < x < R, and f(x) = 0 if x > R or x < − R.
This distribution arises as the limiting distribution of eigenvalues of many random symmetric matrices as the size of the matrix approaches infinity.
It is a scaled beta distribution, more precisely, if Y is beta distributed with parameters α = β = 3/2, then X = 2RY – R has the above Wigner semicircle distribution.
Read more about Wigner Semicircle Distribution: General Properties, Relation To Free Probability
Famous quotes containing the word distribution:
“The man who pretends that the distribution of income in this country reflects the distribution of ability or character is an ignoramus. The man who says that it could by any possible political device be made to do so is an unpractical visionary. But the man who says that it ought to do so is something worse than an ignoramous and more disastrous than a visionary: he is, in the profoundest Scriptural sense of the word, a fool.”
—George Bernard Shaw (1856–1950)