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Empirical Likelihood for Compound Poisson Processes
Author(s) -
Li Zhouping,
Wang Xiping,
Zhou Wang
Publication year - 2012
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2012.00678.x
Subject(s) - independent and identically distributed random variables , mathematics , poisson distribution , empirical likelihood , range (aeronautics) , statistics , compound poisson process , variance (accounting) , econometrics , poisson regression , random variable , poisson process , confidence interval , population , materials science , demography , accounting , sociology , composite material , business
Summary Let { N ( t ), t > 0} be a Poisson process with rate λ > 0, independent of the independent and identically distributed random variablesX 1 , X 2 , … with mean μ and varianceσ 2. The stochastic process∑ j = 1N ( t )X jis 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.