| Title:
|
On multiple normal probabilities of rectangles (English) |
| Author:
|
Anděl, Jiří |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
16 |
| Issue:
|
3 |
| Year:
|
1971 |
| Pages:
|
172-181 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. () |
| MSC:
|
62H99 |
| idZBL:
|
Zbl 0223.62080 |
| idMR:
|
MR0285061 |
| DOI:
|
10.21136/AM.1971.103343 |
| . |
| Date available:
|
2008-05-20T17:50:29Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103343 |
| . |
| Reference:
|
[1] H. Cramér: Mathematical methods of statistics.Princeton, Princeton Univ. Press, 1946. MR 0016588 |
| Reference:
|
[2] R. N. Curnow C. W. Dunnett: The numerical evaluation of certain multivariate normal integrals.Ann. Math. Stat. 33, 1962, 571-579. MR 0137234, 10.1214/aoms/1177704581 |
| Reference:
|
[3] V. Jarník: Integrální počet II.Praha, 1955. |
| Reference:
|
[4] C. R. Rao: Linear statistical inference and its applications.New York, 1966. MR 0221616 |
| Reference:
|
[5] G. P. Steck: A table for computing trivariate normal probabilities.Ann. Math. Stat. 29, 1958, 780-800. Zbl 0088.36101, MR 0093803, 10.1214/aoms/1177706536 |
| Reference:
|
[6] Z. Šidák: Rectangular confidence regions for the means of multivariate normal distributions.Journ. Amer. Stat. Assoc. 62, 1967, 626-633. MR 0216666 |
| . |
