A new unit-bimodal distribution based on correlated Birnbaum-Saunders random variables
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913571088105472 |
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| author | Vila, Roberto Saulo, Helton Quintino, Felipe Zörnig, Peter |
| author_facet | Vila, Roberto Saulo, Helton Quintino, Felipe Zörnig, Peter |
| contents | In this paper, we propose a new distribution over the unit interval which can be characterized as a ratio of the type $Z=Y/(X+Y)$ where $X$ and $Y$ are two correlated Birnbaum-Saunders random variables. The density of $Z$ may be unimodal or bimodal. Simple expressions for the cumulative distribution function, moment-generating function and moments are obtained. Moreover, the stress-strength probability between $X$ and $Y$ is calculated explicitly in the symmetric case, that is, when the respective scale parameters are equal. Two applications of the ratio distribution are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00100 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new unit-bimodal distribution based on correlated Birnbaum-Saunders random variables Vila, Roberto Saulo, Helton Quintino, Felipe Zörnig, Peter Methodology Probability 62E10, 62F10 G.3 In this paper, we propose a new distribution over the unit interval which can be characterized as a ratio of the type $Z=Y/(X+Y)$ where $X$ and $Y$ are two correlated Birnbaum-Saunders random variables. The density of $Z$ may be unimodal or bimodal. Simple expressions for the cumulative distribution function, moment-generating function and moments are obtained. Moreover, the stress-strength probability between $X$ and $Y$ is calculated explicitly in the symmetric case, that is, when the respective scale parameters are equal. Two applications of the ratio distribution are discussed. |
| title | A new unit-bimodal distribution based on correlated Birnbaum-Saunders random variables |
| topic | Methodology Probability 62E10, 62F10 G.3 |
| url | https://arxiv.org/abs/2408.00100 |