Expected Logarithm and Negative Integer Moments of a Noncentral <em>χ</em><sup>2</sup>-Distributed Random Variable
Closed-form expressions for the expected logarithm and for arbitrary negative integer moments of a noncentral <inline-formula><math display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/9/1048 |
| _version_ | 1797553221083856896 |
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| author | Stefan M. Moser |
| author_facet | Stefan M. Moser |
| author_sort | Stefan M. Moser |
| collection | DOAJ |
| description | Closed-form expressions for the expected logarithm and for arbitrary negative integer moments of a noncentral <inline-formula><math display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula>-distributed random variable are presented in the cases of both even and odd degrees of freedom. Moreover, some basic properties of these expectations are derived and tight upper and lower bounds on them are proposed. |
| first_indexed | 2024-03-10T16:12:17Z |
| format | Article |
| id | doaj.art-1886f531418d4beaa2b2243129397b99 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T16:12:17Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-1886f531418d4beaa2b2243129397b992023-11-20T14:18:37ZengMDPI AGEntropy1099-43002020-09-01229104810.3390/e22091048Expected Logarithm and Negative Integer Moments of a Noncentral <em>χ</em><sup>2</sup>-Distributed Random VariableStefan M. Moser0Signal and Information Processing Lab, ETH Zürich, 8092 Zürich, SwitzerlandClosed-form expressions for the expected logarithm and for arbitrary negative integer moments of a noncentral <inline-formula><math display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula>-distributed random variable are presented in the cases of both even and odd degrees of freedom. Moreover, some basic properties of these expectations are derived and tight upper and lower bounds on them are proposed.https://www.mdpi.com/1099-4300/22/9/1048central <i>χ</i><sup>2</sup> distributionchi-square distributionexpected logarithmexponential distributionnegative integer momentsnoncentral <i>χ</i><sup>2</sup> distribution |
| spellingShingle | Stefan M. Moser Expected Logarithm and Negative Integer Moments of a Noncentral <em>χ</em><sup>2</sup>-Distributed Random Variable Entropy central <i>χ</i><sup>2</sup> distribution chi-square distribution expected logarithm exponential distribution negative integer moments noncentral <i>χ</i><sup>2</sup> distribution |
| title | Expected Logarithm and Negative Integer Moments of a Noncentral <em>χ</em><sup>2</sup>-Distributed Random Variable |
| title_full | Expected Logarithm and Negative Integer Moments of a Noncentral <em>χ</em><sup>2</sup>-Distributed Random Variable |
| title_fullStr | Expected Logarithm and Negative Integer Moments of a Noncentral <em>χ</em><sup>2</sup>-Distributed Random Variable |
| title_full_unstemmed | Expected Logarithm and Negative Integer Moments of a Noncentral <em>χ</em><sup>2</sup>-Distributed Random Variable |
| title_short | Expected Logarithm and Negative Integer Moments of a Noncentral <em>χ</em><sup>2</sup>-Distributed Random Variable |
| title_sort | expected logarithm and negative integer moments of a noncentral em χ em sup 2 sup distributed random variable |
| topic | central <i>χ</i><sup>2</sup> distribution chi-square distribution expected logarithm exponential distribution negative integer moments noncentral <i>χ</i><sup>2</sup> distribution |
| url | https://www.mdpi.com/1099-4300/22/9/1048 |
| work_keys_str_mv | AT stefanmmoser expectedlogarithmandnegativeintegermomentsofanoncentralemchemsup2supdistributedrandomvariable |