The Semicircle Distribution is the probability distribution supported on the interval [−R, R] 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):

Random variable X has the standard semicircle distribution if X has a continuous distribution on [−1,1] with probability density function g given by

f(x;mu,r) = 2*sqrt(r**2 - (x-mu)**2)/(PI*r**2)
mu - r