Sampling from a Levy distribution is done using an inverse transform of the cumulative distribution function of the standard normal distribution.
With u a uniform deviate in [0, 1). An alternative is direct generation of a uniform normal variate with mean 0 and standard deviation 1: N(0, 1):
This should be faster than inverse transform sampling if generation of the normal distribution sample is faster than computation of the inverse cumulative probability function.
This sampler can be used in Commons Statistics for the Levy distribution.
The extremes of the support should be investigated, i.e. what is the maximum value for a sample from a standard normal distribution such as the ZigguratNormalizedGaussianSampler vs the maximum value of the inverse CDF of the normal distribution when the uniform deviate is at the upper limit of 1 - 2^-53.