WOLFRAM|DEMONSTRATIONS PROJECT

Stable Density Function

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α - shape
1.5
β - skewness
-1
γ - scale
1
δ - location
0
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.