The distribution of the sample correlation coefficient under variance-truncated normality
The non-null distribution of the sample correlation coefficient under bivariate normality is derived when each of the associated two sample variances is subject to stripe truncation including usual single and double truncation as special cases. The probability density function is obtained using seri...
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| Published in | Metrika Vol. 87; no. 5; pp. 471 - 497 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.07.2024
Springer Nature B.V |
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| Abstract | The non-null distribution of the sample correlation coefficient under bivariate normality is derived when each of the associated two sample variances is subject to stripe truncation including usual single and double truncation as special cases. The probability density function is obtained using series expressions as in the untruncated case with new definitions of weighted hypergeometric functions. Formulas of the moments of arbitrary orders are given using the weighted hypergeometric functions. It is shown that the null joint distribution of the sample correlation coefficients under multivariate untruncated normality holds also in the variance-truncated cases. Some numerical illustrations are shown. |
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| AbstractList | The non-null distribution of the sample correlation coefficient under bivariate normality is derived when each of the associated two sample variances is subject to stripe truncation including usual single and double truncation as special cases. The probability density function is obtained using series expressions as in the untruncated case with new definitions of weighted hypergeometric functions. Formulas of the moments of arbitrary orders are given using the weighted hypergeometric functions. It is shown that the null joint distribution of the sample correlation coefficients under multivariate untruncated normality holds also in the variance-truncated cases. Some numerical illustrations are shown. |
| Author | Ogasawara, Haruhiko |
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| Cites_doi | 10.2307/2334076 10.1016/j.jmva.2017.02.011 10.1007/s00184-020-00802-1 10.1214/aoms/1177704016 10.1016/j.jmva.2021.104729 10.1080/03610926.2012.735324 10.1080/10618600.2017.1322092 10.1080/03610929208830890 10.1111/j.2517-6161.1965.tb01497.x 10.1002/9780470316559 10.1007/s11009-018-9622-7 10.3844/jmssp.2016.12.22 10.1080/03610926.2020.1867742 10.2307/3315434 10.1111/j.2517-6161.1953.tb00135.x 10.1111/j.2517-6161.1961.tb00408.x 10.1080/07474939908800447 10.1017/CBO9780511550683 10.1501/Commua1_0000000322 10.1002/0471722065 10.1007/s00184-023-00918-0 |
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| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Keywords | Stripe truncation Multivariate normality Sample variances and covariances Multivariate gamma function Weighted hypergeometric functions Wishart distribution |
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| SubjectTerms | Bivariate analysis Correlation coefficients Economic Theory/Quantitative Economics/Mathematical Methods Hypergeometric functions Mathematics and Statistics Normality Probability density functions Probability Theory and Stochastic Processes Statistics Variance |
| Title | The distribution of the sample correlation coefficient under variance-truncated normality |
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