α-Laplace processes

Jayakumar, K.; Kalyanaraman, Kaushik; Pillai, R. N.

doi:10.1016/0895-7177(95)00105-b

Cited by 19 publications

(11 citation statements)

References 5 publications

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“…The class of probability distributions with density functions p α,ν,θ (x) corresponding to ch.f. (3) have found some interesting properties and applications, see [1,2,6,11,[27][28][29]32] and related papers. In particular, they are good candidates to model financial data which exhibits high kurtosis and heavy tails [36].…”

Section: The Linnik Distributionsmentioning

confidence: 99%

On Mixture Representations for the Generalized Linnik Distribution and Their Applications in Limit Theorems

2020

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We present new mixture representations for the generalized Linnik distribution in terms of normal, Laplace, exponential and stable laws and establish the relationship between the mixing distributions in these representations. Based on these representations, we prove some limit theorems for a wide class of rather simple statistics constructed from samples with random sized including, e. g., random sums of independent random variables with finite variances and maximum random sums, in which the generalized Linnik distribution plays the role of the limit law. Thus we demonstrate that the scheme of geometric (or, in general, negative binomial) summation is far not the only asymptotic setting (even for sums of independent random variables) in which the generalized Linnik law appears as the limit distribution.

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Section: The Linnik Distributionsmentioning

confidence: 99%

On Mixture Representations for the Generalized Linnik Distribution and Their Applications in Limit Theorems

2020

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“…Jayakumar et al (1995) developed an algorithm for generating α-Laplace processes with the help of some well-known results in Devroye (1990). The algorithm for generating the GNLAR(1) process for integer values of δ is given below:…”

Section: Appendixmentioning

confidence: 99%

Generalized normal-Laplace AR process

Tomy

Jose

2009

Statistics & Probability Letters

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“…Jayakumar et al (1995) developed an algorithm to generate Linnik random variables. In a similar manner the PGLAR (1) process can be generated using computers.…”

Section: Pakes Generalized Linnik Distribution and Processesmentioning

confidence: 99%

“…Kozubowski (2000) discussed the fractional moment estimation of Linnik parameters. Jayakumar et al (1995) generalized the Laplace processes of Lawrance (1978) and Dewald and Lewis (1985). Kotz et al (2001) discuss various generalizations of the Laplace distributions.…”

Section: Introductionmentioning

confidence: 98%