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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.10111 |
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| _version_ | 1866914869989605376 |
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| author | Rao, B. L. S. Prakasa |
| author_facet | Rao, B. L. S. Prakasa |
| contents | Kotlarski (1978) proved a result on identification of the distributions of independent random variables $X,Y$ and $Z$ from the joint distribution of the bivariate random vector $(U,V)$ where $(U,V)= (\max(X,Z),\max(Y,Z)).$ We extend this result to the case $(U,V)=(\max(X,aZ_1,bZ_2),\max(Y,cZ_1,dZ_2))$ where $X,Y,Z_1,Z_2$ are independent or max-independent random variables, $Z_1$ and $Z_2$ are identically distributed and $a,b,c,d$ are known positive constants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10111 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a characterization of probability distribution based on maxima of independent or max-independent random variables Rao, B. L. S. Prakasa Probability 62E10 Kotlarski (1978) proved a result on identification of the distributions of independent random variables $X,Y$ and $Z$ from the joint distribution of the bivariate random vector $(U,V)$ where $(U,V)= (\max(X,Z),\max(Y,Z)).$ We extend this result to the case $(U,V)=(\max(X,aZ_1,bZ_2),\max(Y,cZ_1,dZ_2))$ where $X,Y,Z_1,Z_2$ are independent or max-independent random variables, $Z_1$ and $Z_2$ are identically distributed and $a,b,c,d$ are known positive constants. |
| title | On a characterization of probability distribution based on maxima of independent or max-independent random variables |
| topic | Probability 62E10 |
| url | https://arxiv.org/abs/2407.10111 |