By Aleksander Janicki
ISBN-10: 0824788826
ISBN-13: 9780824788827
Provides new laptop equipment in approximation, simulation, and visualization for a bunch of alpha-stable stochastic methods.
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Extra info for Simulation and chaotic behavior of [alpha]-stable stochastic processes
Example text
111Mri• rW. O D. 2. 1}. 3. 1}. 4. 30. 5. 45. 47 A. JANICKI and A. 5 Computer Generation of a—Stable Distributions When we start working with a-stable distributions, the main problem is that, except for a few values of four parameters describing the characteristic function, their density functions are not known explicitly. ) As we know, the LePage series representations are not the most suited for an application in computer calculations, so our aim is to describe now a few of the possible general techniques of constructing and computer simulating stable random variables.
Tail Probabilities from the sample of 2000 "trials". 2. Tail Probabilities from the sample of 4000 "trials". 141 Computer generator of skewed a-stab le variables. ). 2) and = , 43 arc tan(0 tan(ra/2)) 1— 1-- al [cos(arc tan(0 tan(7ra/2)))1 -1 /'. Generalizing the result of Kanter (1975) or slightly modifying the algorithm of Chambers, Mallows and Stuck (1976), one can see that Y belongs to the class of S„(1, 3, 0) random variables. 2) as a good technique of computer simulation of a-stable random variables, stochastic measures and processes of different kinds.
JANICKI and A. 3. 1835. 4. Function f j 3 = fL(x,y); P{S0 . 2297. ( . 1. 1) give an idea of an extension of the well-known "rule of 3 a's" for normal standard distributions to the case of stable variables. ) Without developing any necessary mathematical formalism let us mention that lirrlSa = Z, where Z is described by the following conditions: P{Z = 0} = p. P{Z = +oo} = q/2, P{Z = -oo} = q/2, with p > 0, q > 0 and p + q = I. When looking at the data presented in this section one can imagine what is going on when we simulate stable variables on a computer for changing values of the parameter a.
Simulation and chaotic behavior of [alpha]-stable stochastic processes by Aleksander Janicki
by Daniel
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