Demo of Skew Lognormal Cascade Distribution: Have fun playing!

If you don't know where to start, try η = 0.5, β = -0.3, g = 0.1.
That is approximately the parameters for the US stock market.
The tail gets fatter rapidly when η > 0.5.

Numerical

Theoretical

mean =

0.0000

0.0000

std =

1.0000

1.0000

variance =

1.0000

1.0000

skewness =

-0.0000

0.0000

kurtosis =

-0.0000

0.0000

sum(pdf) =

1.0000

1.0000

delta_x =

1/30

x_range =

[-20,20]

The drop at the very last bit of the right tail is
due to lack of data beyond the range. It does NOT reflect
the real tail behavior.