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On evaluation of some two-dimensional normal probabilities
Applications of Mathematics, Tome 19 (1974) no. 1, pp. 28-35 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.1974.103511
Classification : 60E05, 62E10, 62E99, 62H99 
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Anděl, Jiří. On evaluation of some two-dimensional normal probabilities. Applications of Mathematics, Tome 19 (1974) no. 1, pp. 28-35. doi: 10.21136/AM.1974.103511

[1] Anděl J. (1971): On multiple normal probabilities of rectangles. Aplikace matematiky 16, 172-181. | MR

[2] Cramér H., Leadbetter M. R. (1967): Stationary and related stochastic processes. Wiley, New York. | MR

[3] Smirnov N. V., Bolšev L. N. (1962): Tablicy dlja vyčislenija funkcii dvumernogo normalnogo raspredelenija. Izd. Akademii nauk SSSR. | MR

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