Stable Density Function

α - shape

1.5

β - skewness

-1

γ - scale

1

δ - location

0

-15

-10

-5

0

5

10

15

0.1

0.2

0.3

0.4

0.5

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

α

is the distribution shape parameter, a positive value less than or equal to 2. For

α=2

the result is the normal distribution.

α

is the tail exponent of the distribution: lower values give fatter tails.

β

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

γ

is the scale parameter.

δ

is the location parameter.

The routine used can result in numeric instabilities for small values of

α

and so a reduced range is used.