The standard uniform distribution (lower = 0 and upper = 1) is a special case of the beta distribution obtained by setting the beta distribution parameters a = 1 and b = 1.
The inversion method uses the continuous standard uniform distribution to generate random numbers for any other continuous distribution. The inversion method relies on the principle that continuous cumulative distribution functions (cdfs) range uniformly over the open interval (0,1). If u is a uniform random number on (0,1), then x = F–1(u) generates a random number x from any continuous distribution with the specified cdf F.