XploRe Help : pdfstab

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	distribs
See also:	cdfstab

Quantlet:		pdfstab
Description:		computes probability density function of stable distribution

Reference(s):

[1] J.P. Nolan (1997) "Numerical computation of stable densities and distribution function", Commun.Stat.:Stochastic Models 13:759-774 [2] R.Weron (1995) "Performance of the estimators of stable law parameters", Research Report HSC/95/1, www.im.pwr.wroc.pl\~hugo\Publications.html

Usage:	`z=pdfstab(x,alpha,sigma,beta,{mu})`
Input:
	`x`	input array
	`alpha`	array, characteristic exponent
	`sigma`	array, the scale parameter
	`beta`	array, the skewness parameter
	`mu`	array, the location parameter ; default value is 0
Output:
	`y`	array of stable probability distribution function

Note:

For 0.98 < alpha < 1.02 the stable pdf is calculated as a linear combination using the formula for alpha = 1 and alpha = 1.02 or 0.98, otherwise numerical errors creep in. Linear approximation is also used near mu.

Example:

library("distribs") x = -1:1 pdfstab(x, 1.5, 1, 0.5, 0)

Result:

[1,]  0.26805
[2,]  0.25411
[3,]  0.14151

Author: Szymon Borak, Rafal Weron, 021205