The stable density function in these routines is calculated using the fast Fourier transform. The Nolan 0-parameterization is used.

is the distribution shape parameter, a positive value less than or equal to 2. For the result is the normal distribution. is the tail exponent of the distribution: lower values give fatter tails.

is the skewness parameter in the range (-1, 1).

is the scale parameter.

is the location parameter.

The routine used can result in numeric instabilities for small values of and so a reduced range is used.