Boundary crossing of order statistics point processes

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• 作者：Pierre-Olivier Goffard ; ^{pierre.olivier.goffard@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Claude Lefè ; vre
• 关键词：Order statistic property ; Lower and upper boundaries ; Appell and Abel&ndash ; Gontcharoff polynomials
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：447
• 期：2
• 页码：890-907
• 全文大小：1013 K

文摘

This paper is concerned with the first crossing of an order statistic point process through general moving boundaries. Our purpose is to determine exact boundary crossing probabilities in both one and two boundary cases. Simple recursive methods are obtained that exploit an underlying algebraic structure of polynomial type. This structure is a direct consequence of the order statistic property. The proposed approach is easy to implement and efficient. Perspectives in statistics are also announced.