Mena, R.H. and Walker, S.G. (2004) A density function connected with a non-negative self-decomposable random variable. Journal of Statistical Computation and Simulation, 74 (10). pp. 765-775. ISSN 0094-9655 .
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The innovation random variable for a non-negative self-decomposable random variable can have a compound Poisson distribution. In this case, we provide the density function for the compounded variable. When it does not have a compound Poisson representation, there is a straightforward and easily available compound Poisson approximation for which the density function of the compounded variable is also available. These results can be used in the simulation of Ornstein-Uhlenbeck type processes with given marginal distributions. Previously, simulation of such processes used the inverse of the corresponding tail Levy measure. We show this approach corresponds to the use of an inverse cdf method of a certain distribution. With knowledge of this distribution and hence density function, the sampling procedure is open to direct sampling methods.
|Uncontrolled keywords:||infinite divisibility; Ornstein-Uhlenbeck type process; self-decomposable; shot noise|
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics|
|Depositing User:||Judith Broom|
|Date Deposited:||26 Sep 2008 14:20|
|Last Modified:||14 Jan 2010 14:40|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/10583 (The current URI for this page, for reference purposes)|
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