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Title: Empirical Likelihood for Compound Poisson Processes
Authors: Li, Z.
Wang, X.
Zhou, W. 
Keywords: Compound Poisson process
Confidence interval
Empirical likelihood
Poisson process
Issue Date: Dec-2012
Citation: Li, Z., Wang, X., Zhou, W. (2012-12). Empirical Likelihood for Compound Poisson Processes. Australian and New Zealand Journal of Statistics 54 (4) : 463-474. ScholarBank@NUS Repository.
Abstract: Summary: Let {N(t), t > 0} be a Poisson process with rate λ > 0, independent of the independent and identically distributed random variables X1,X2,... with mean μ and variance σ2. The stochastic process ∑j=1 N(t)Xj is then called a compound Poisson process and has a wide range of applications in, for example, physics, mining, finance and risk management. Among these applications, the average number of objects, which is defined to be λμ, is an important quantity. Although many papers have been devoted to the estimation of λμ in the literature, in this paper, we use the well-known empirical likelihood method to construct confidence intervals. The simulation results show that the empirical likelihood method often outperforms the normal approximation and Edgeworth expansion approaches in terms of coverage probabilities. A real data set concerning coal-mining disasters is analyzed using these methods. © 2012 Australian Statistical Publishing Association Inc. Published by Wiley Publishing Asia Pty Ltd.
Source Title: Australian and New Zealand Journal of Statistics
ISSN: 13691473
DOI: 10.1111/j.1467-842X.2012.00678.x
Appears in Collections:Staff Publications

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