Geodesic
On multiple normal probabilities of rectangles
Applications of Mathematics, Tome 16 (1971) no. 3, pp. 172-181
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Denote $A$ a symmetric interval in the $n$-dimensional Euclidean space. Let the random vector $X$ have $n$-dimensional normal distribution with vanishing expectation and regular covariance matrix. A method for the numerical evaluation of the probability $P(A)=P(X\in A)$ is suggested in the paper. $P(A)$ is expressed as the sum of an infinite series. The bounds for the remainder term are given. The rate of convergence is analysed in detail in the twodimensional case. Two numerical examples are given to compare derived results with other methods.
Denote $A$ a symmetric interval in the $n$-dimensional Euclidean space. Let the random vector $X$ have $n$-dimensional normal distribution with vanishing expectation and regular covariance matrix. A method for the numerical evaluation of the probability $P(A)=P(X\in A)$ is suggested in the paper. $P(A)$ is expressed as the sum of an infinite series. The bounds for the remainder term are given. The rate of convergence is analysed in detail in the twodimensional case. Two numerical examples are given to compare derived results with other methods.
DOI : 10.21136/AM.1971.103343
Classification : 62H99 
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Anděl, Jiří. On multiple normal probabilities of rectangles. Applications of Mathematics, Tome 16 (1971) no. 3, pp. 172-181. doi: 10.21136/AM.1971.103343

[1] H. Cramér: Mathematical methods of statistics. Princeton, Princeton Univ. Press, 1946. | MR

[2] R. N. Curnow C. W. Dunnett: The numerical evaluation of certain multivariate normal integrals. Ann. Math. Stat. 33, 1962, 571-579. | DOI | MR

[3] V. Jarník: Integrální počet II. Praha, 1955.

[4] C. R. Rao: Linear statistical inference and its applications. New York, 1966. | MR

[5] G. P. Steck: A table for computing trivariate normal probabilities. Ann. Math. Stat. 29, 1958, 780-800. | DOI | MR | Zbl

[6] Z. Šidák: Rectangular confidence regions for the means of multivariate normal distributions. Journ. Amer. Stat. Assoc. 62, 1967, 626-633. | MR

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