Stable Distribution Function

shape α

1.5

skewness β

-1

scale γ

1

location δ

0

The simple algorithm used in this Demonstration can calculate the stable distribution function and its first several derivatives with good accuracy for

α>1

. It is offered to help with financial analysis where the data generally has the shape parameter greater than 1. The Nolan 1-parameterization is used where the parameters have the characteristics listed below.

α

is the distribution shape parameter,

0<α≤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; when

α>1

as in this Demonstration

δ

is the expectation of the distribution.