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Normal and poisson approximation of infinitely divisible distribution functions

 

作者: U. Lorz,   L. Heinrich,  

 

期刊: Statistics  （Taylor Available online 1991）
卷期: Volume 22, issue 4  

页码: 327-349

 

ISSN:0233-1888

 

年代: 1991

 

DOI:10.1080/02331889108802342

 

出版商: Akademie-Verlag

 

关键词: Primary 60F05;Secondary 60E07;Infinitely divisible distributions;EDGEWORTH and POISSON–CHARLIER expansion;POISSON shor noise representation;log–likelihood ratio test

 

数据来源: Taylor

 

摘要:

The main purpose of this paper is to present bounds of the discrepancy between an infinitely divisible distribution function with finite second moment and the normal as well as the poisson distribution function. Special emphasise is put on explicit numerical constancts involved in the error bounds. To improve these estimates an EDGEWORTH expansion in the smooth case and a POISSON–CHARLEIR expansion in the lattice case are developed. Some applications to the POISSON shot noise illustrate the obtained results

 

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