Let F(x) be Gaussian cdf, and f(x) be the density. According to Abramowitz and Stegum p954, if x is observed with small error, Delta F(x)=f(x) Delta x where Delta x is the difference operator.
Let x be a vector of N(0,1) variables sorted from smallest to largest. I am interested in the difference between the CDF of two consecutive (normal) variables in the ordered sequence. say, j and j-1. The A-S result suggests F(j)-F(j-1)= f(j) [x(j)-x(j-1)] But this seems to suggest F(x) for the ordered series is a random walk. Is this a correct use of A-S, and is this a known result? Thanks in advance. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
