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Summary:
Let $P_r\{.\}$ be the probability measure corresponding to a two-dimensional normal distribution with zero means, unit variances and the correlation coefficient $r$. A method for numerical evaluation of the probabilities $P_r\{(-a,a)\times (-a,a)\}$ and $P_r\{(-\infty,a)\times (-\infty,a)\}$ is suggested in the paper, which is particularly advantageous when $r$ is near to 1 or -1.
References:
[1] Anděl J. (1971): On multiple normal probabilities of rectangles. Aplikace matematiky 16, 172-181. MR 0285061
[2] Cramér H., Leadbetter M. R. (1967): Stationary and related stochastic processes. Wiley, New York. MR 0217860
[3] Smirnov N. V., Bolšev L. N. (1962): Tablicy dlja vyčislenija funkcii dvumernogo normalnogo raspredelenija. Izd. Akademii nauk SSSR. MR 0150925
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