Suppose X, Y1 and Y2 are independently Normally distributed with
means 0, mu and mu, and each has variance 1. Then Pr[X < Y1] is
easily obtained as the tail area of a Gaussian distribution with
variance 2, for which good algorithms are of course readily
available.
The quantity Pr[X < both Y1 and Y2] is also of interest. It can be
expressed as an integral in an obvious manner, but this doesn't
appear to simplify in any useful way - which fits in with Kendall &
Stuart's comments about the intractability of order statistics in the
Gaussian case. Can anyone suggest a tractable algorithm to calculate
Pr[X < Y1 and Y2] for any real value of mu, please? A series
expansion with sufficient terms to get about 8-figure precision would
be ideal. The rest of my programming is in Fortran.
Many thanks.
Robert Newcombe.
..........................................
Robert G. Newcombe, PhD, CStat, Hon MFPHM
Reader in Medical Statistics
University of Wales College of Medicine
Heath Park
Cardiff CF14 4XN, UK.
Phone 029 2074 2329 or 2311
Fax 029 2074 3664
Email [log in to unmask]
Web:
http://www.uwcm.ac.uk/epidemiology_statistics/research/statistics/newc
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