Autoregressive processes with Pakes and geometric Pakes generalized Linnik marginals

Lekshmi, V. Seetha; Jose, Kim

doi:10.1016/j.spl.2005.08.013

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2006

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Cited by 13 publications

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“…play an important role in some characterization problems of mathematical statistics. The class of probability distributions with density functions p α,ν,θ (x) have found some interesting properties and applications [2,4,5,7,8,9,24,29,30,32,33,34,35,36,37,38,41,43,44,45,51,52,60,61,64,65,66,68]. In particular, they are good candidates to model financial data which exhibits high kurtosis and heavy tails.…”

Section: Introductionmentioning

confidence: 99%

Analytic and Asymptotic Properties of Multivariate Generalized Linnik’s Probability Densities

Lim

Teo

2009

J Fourier Anal Appl

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This paper studies the properties of the probability density function p α,ν,n (x) of the n-variate generalized Linnik distribution whose characteristic function ϕ α,ν,n (t) is given bywhere t is the Euclidean norm of t ∈ R n . Integral representations of p α,ν,n (x) are obtained and used to derive the asymptotic expansions of p α,ν,n (x) when x → 0 and x → ∞ respectively. It is shown that under certain conditions which are arithmetic in nature, p α,ν,n (x) can be represented in terms of entire functions.

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