Confidence disc and square for Cauchy distributions
UDC 519.21 We  construct a confidence region of parameters for a sample of size $N$ from the Cauchy distributed random variables. Although Cauchy distribution has two parameters, a location parameter $\mu \in\mathbb{R}$ and a scale parameter $\sigma > 0,$ w...
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| Date: | 2023 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6797 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512513199702016 |
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| author | Akaoka, Y. Okamura, K. Otobe, Y. Akaoka, Y. Okamura, K. Otobe, Y. |
| author_facet | Akaoka, Y. Okamura, K. Otobe, Y. Akaoka, Y. Okamura, K. Otobe, Y. |
| author_sort | Akaoka, Y. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-04-15T15:10:30Z |
| description |
UDC 519.21
We  construct a confidence region of parameters for a sample of size $N$ from the Cauchy distributed random variables. Although Cauchy distribution has two parameters, a location parameter $\mu \in\mathbb{R}$ and a scale parameter $\sigma > 0,$ we infer them simultaneously by regarding them as a single complex parameter $\gamma := \mu + i\sigma.$ The region should be a domain in the complex plane. We give a simple and concrete formula to give the region as a disc and as a square. |
| doi_str_mv | 10.37863/umzh.v75i3.6797 |
| first_indexed | 2026-03-24T03:29:59Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6797 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:29:59Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-67972023-04-15T15:10:30Z Confidence disc and square for Cauchy distributions Confidence disc and square for Cauchy distributions Akaoka, Y. Okamura, K. Otobe, Y. Akaoka, Y. Okamura, K. Otobe, Y. confidence disc Cauchy distribution central limit theorem Mathematical Statistics UDC 519.21 We  construct a confidence region of parameters for a sample of size $N$ from the Cauchy distributed random variables. Although Cauchy distribution has two parameters, a location parameter $\mu \in\mathbb{R}$ and a scale parameter $\sigma > 0,$ we infer them simultaneously by regarding them as a single complex parameter $\gamma := \mu + i\sigma.$ The region should be a domain in the complex plane. We give a simple and concrete formula to give the region as a disc and as a square. УДК 519.21 Довірчий диск і квадрат для розподілів Коші Побудовано довірчу область параметрів для вибірки розміром $N$ для  випадкових величин з розподілом Коші. Хоча розподіл Коші має два параметри, параметр розташування $\mu \in\mathbb{R}$ і параметр масштабу $\sigma > 0,$ введено їх одночасно як єдиний комплексний параметр  $\gamma := \mu + i\sigma.$ Область, що розглядається, повинна бути областю в комплексній площині. Наведено просту і конкретну формулу, за допомогою якої цю область можна подати  як диск або квадрат.  Institute of Mathematics, NAS of Ukraine 2023-04-11 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/6797 10.37863/umzh.v75i3.6797 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 3 (2023); 305 - 318 Український математичний журнал; Том 75 № 3 (2023); 305 - 318 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6797/9786 Copyright (c) 2023 Kazuki Okamura |
| spellingShingle | Akaoka, Y. Okamura, K. Otobe, Y. Akaoka, Y. Okamura, K. Otobe, Y. Confidence disc and square for Cauchy distributions |
| title | Confidence disc and square for Cauchy distributions |
| title_alt | Confidence disc and square for Cauchy distributions |
| title_full | Confidence disc and square for Cauchy distributions |
| title_fullStr | Confidence disc and square for Cauchy distributions |
| title_full_unstemmed | Confidence disc and square for Cauchy distributions |
| title_short | Confidence disc and square for Cauchy distributions |
| title_sort | confidence disc and square for cauchy distributions |
| topic_facet | confidence disc Cauchy distribution central limit theorem Mathematical Statistics |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6797 |
| work_keys_str_mv | AT akaokay confidencediscandsquareforcauchydistributions AT okamurak confidencediscandsquareforcauchydistributions AT otobey confidencediscandsquareforcauchydistributions AT akaokay confidencediscandsquareforcauchydistributions AT okamurak confidencediscandsquareforcauchydistributions AT otobey confidencediscandsquareforcauchydistributions |