I am using the ADinf procedure of Marsaglia & Marsaglia to compute the CDF of the Anderson Darling statistic. I am interested in the survival function, 1 minus the CDF, for large values of the test statistic. The implementation given by Marsaglia & Marsaglia does well up until roundoff issues creep in around $z=30$:
This is somewhat to be expected. I was wondering, however, if the asymptotics of this function are known. If so, I could just approximate the tail for $z \ge 30$. Alternatively, if there is an implementation of the CDF that gives the upper tail, I would be happy with that.
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1
An asymptotic form for the AD distribution in
C.D. Sinclair and B.D. Spurr, Journal of the American statistical association, 83, p. 1190-1191, (1988)
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3$\begingroup$ In referencing this paper, the Marsaglia and Marsaglia paper (2004) states that this asymptotic expression "also suffers from lack of a method for its accurate determination." $\endgroup$– whuber ♦Jan 10, 2012 at 19:14