ON THE POWER FUNCTION OF THE LRT AGAINST ONE-SIDED AND TWO-SIDED ALTERNATIVES IN BIVARIATE NORMAL DISTRIBUTION
This paper addresses the problem of testing simple hypotheses about the mean of a bivariate normal distribution with identity covariance matrix against restricted alternatives. The LRTs and their power functions for such types of hypotheses are derived. Furthermore, through some elementary calculus,...
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| Format: | Article |
|---|---|
| Language: | English |
| Published: |
University of Tehran
1996-12-01
|
| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31136_3127bd4388edcb3d2ef009a0af36cb17.pdf |
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| collection | DOAJ |
| description | This paper addresses the problem of testing simple hypotheses about the mean of
a bivariate normal distribution with identity covariance matrix against restricted
alternatives. The LRTs and their power functions for such types of hypotheses are
derived. Furthermore, through some elementary calculus, it is shown that the power
function of the LRT satisfies certain monotonicity and symmetry properties. We treat
two cases, the case of one-sided alternatives restricted to some closed convex cone,
and the case of two-sided alternatives restricted to a two-sided cone |
| format | Article |
| id | doaj-art-2b9c78f796664d9ebf9f85f791d006fe |
| institution | DOAJ |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 1996-12-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-2b9c78f796664d9ebf9f85f791d006fe2025-08-20T03:08:48ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69141996-12-017431136ON THE POWER FUNCTION OF THE LRT AGAINST ONE-SIDED AND TWO-SIDED ALTERNATIVES IN BIVARIATE NORMAL DISTRIBUTIONThis paper addresses the problem of testing simple hypotheses about the mean of a bivariate normal distribution with identity covariance matrix against restricted alternatives. The LRTs and their power functions for such types of hypotheses are derived. Furthermore, through some elementary calculus, it is shown that the power function of the LRT satisfies certain monotonicity and symmetry properties. We treat two cases, the case of one-sided alternatives restricted to some closed convex cone, and the case of two-sided alternatives restricted to a two-sided conehttps://jsciences.ut.ac.ir/article_31136_3127bd4388edcb3d2ef009a0af36cb17.pdf |
| spellingShingle | ON THE POWER FUNCTION OF THE LRT
AGAINST ONE-SIDED AND TWO-SIDED
ALTERNATIVES IN BIVARIATE NORMAL
DISTRIBUTION Journal of Sciences, Islamic Republic of Iran |
| title | ON THE POWER FUNCTION OF THE LRT
AGAINST ONE-SIDED AND TWO-SIDED
ALTERNATIVES IN BIVARIATE NORMAL
DISTRIBUTION |
| title_full | ON THE POWER FUNCTION OF THE LRT
AGAINST ONE-SIDED AND TWO-SIDED
ALTERNATIVES IN BIVARIATE NORMAL
DISTRIBUTION |
| title_fullStr | ON THE POWER FUNCTION OF THE LRT
AGAINST ONE-SIDED AND TWO-SIDED
ALTERNATIVES IN BIVARIATE NORMAL
DISTRIBUTION |
| title_full_unstemmed | ON THE POWER FUNCTION OF THE LRT
AGAINST ONE-SIDED AND TWO-SIDED
ALTERNATIVES IN BIVARIATE NORMAL
DISTRIBUTION |
| title_short | ON THE POWER FUNCTION OF THE LRT
AGAINST ONE-SIDED AND TWO-SIDED
ALTERNATIVES IN BIVARIATE NORMAL
DISTRIBUTION |
| title_sort | on the power function of the lrt against one sided and two sided alternatives in bivariate normal distribution |
| url | https://jsciences.ut.ac.ir/article_31136_3127bd4388edcb3d2ef009a0af36cb17.pdf |