| Title:
|
On a probability inequality for multivariate normal distribution (English) |
| Author:
|
Das Gupta, Somesh |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
21 |
| Issue:
|
1 |
| Year:
|
1976 |
| Pages:
|
1-4 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let two random vectors $X_1$ and $X_2$ be jointly distributed as a normal distribution with mean $\mu$ and covariance matrix $\sum_1$. Let $\Pi (\lambda)$be the probability that $X_1\in C_1, X_2\in C_2$, where $C_1$ and $C_2$ are convex symmetric sets, when the covariance matrix between $X_1$ and $X_2$ is multiplied by $\lambda;0\leq \lambda \leq 1$. It is shown that $\Pi(\lambda)$ increases with $\lambda$ under some conditions on $\mu$ and $\sum_1$. This generalizes the results of Das Gupta et al (1972), Khatri (1967) and Šidák (1973). () |
| MSC:
|
26D15 |
| MSC:
|
52A20 |
| MSC:
|
60E05 |
| MSC:
|
62H05 |
| MSC:
|
62H99 |
| idZBL:
|
Zbl 0362.60037 |
| idMR:
|
MR0391382 |
| DOI:
|
10.21136/AM.1976.103618 |
| . |
| Date available:
|
2008-05-20T18:03:08Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103618 |
| . |
| Reference:
|
[1] Das Gupta S., Eaton M. L., Olkin I., Perlman M. D., Savage L. J., and Sobel M.: Inequalities on the probability content of convex regions for elliptically contoured distributions.Proc. Sixth Berk. Symp. on Math. Stat. and Prob. Vol. 11, (1972), 241-265. MR 0413364 |
| Reference:
|
[2] Khatri C. G.: On certain inequalities for normal distributions and their applications to simultaneous confidence bounds.Ann. Math. Statist. 38, (1967), 1853-1867. Zbl 0155.27103, MR 0220392, 10.1214/aoms/1177698618 |
| Reference:
|
[3] Šidák Z.: On probabilities in certain multivariate distributions: their dependence on correlations.Aplikace Matematiky 18, (1973), 128-135. MR 0314197 |
| . |
