More Functions

This is the density function used for FLogLikelihood and FMLFit.  It takes two options SR and NN that are passed to them by the FMLFit algorithm.

The functions can be used arbitrarily close to α = 1.

Very accurate results are theoretically possible by increasing the working precsion and using rational number inputs here is an example of calculations on the light tail of a maximally skewed stable distribution.

2	0.2735494622587961895097753415393131318581857529865089662325715423.
4	0.03859887951674424956992458391787071656036706595528394723586806156.
8	3.39197913938740192130388887330711786923890136194690806320001752.99999999999999*^-25
16	1.29212806987684368312168400775160175243211559726691771060093099.99999999999999*^-496
32	1.490782327643959614250326557904942392057212973554181366442874574.00000000000122*^-10006
64	1.28876881056847406907355147746013211220193021391578303065761305.99999999999246*^-201721

SMode is provided to help determine where the mode may be in the 1-parameterization.  It uses FindRoot get the value of x when the first derivative equals 0.  It has some trouble when α < 0.5 && Abs[β] == 1.

This function is used for the SMode calculation above.  A first derivative formula is numerically integrated.

© Copyright 2007 mathestate    Fri 14 Dec 2007