JSM 2004 Online Program

Abstract #301799

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Activity Number:	19
Type:	Contributed
Date/Time:	Sunday, August 8, 2004 : 2:00 PM to 3:50 PM
Sponsor:	Section on Nonparametric Statistics
Abstract - #301799
Title:	The Reflection Principle Revisited
Author(s):	John L. Stedl*+
Companies:	Chicago State University
Address:	College of Business, Chicago, IL, 60628,
Keywords:	Reflection Principle ; random walk ; path
Abstract:	In his classic book on probability, the great William Feller introduced the Reflection Principle. It states that the number of paths from (x,y) to (u,v) which touch or cross the x-axis is equal to the number of paths from the reflected point (x,-y) to (u,v),where (x,y) and (u,v) are integral points in the positive quadrant: u>x>=0, y>0, v>0 . The purpose of this paper is to obtain the probability distribution of the number of times the x-axis is crossed for all paths from (0,0) to (0,2n). The distribution is derived by repeated applications of the Reflection Principle. The mean and standard deviation of this random variable are derived. Finally, a quality control application using this result is presented.

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