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The distribution of the sample correlation coefficient under variance-truncated normality

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  • Haruhiko Ogasawara

    (Otaru University of Commerce)

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.

Suggested Citation

  • Haruhiko Ogasawara, 2024. "The distribution of the sample correlation coefficient under variance-truncated normality," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(5), pages 471-497, July.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:5:d:10.1007_s00184-023-00918-0
    DOI: 10.1007/s00184-023-00918-0
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    References listed on IDEAS

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    1. Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 287-330.
    2. Arismendi, Juan C. & Broda, Simon, 2017. "Multivariate elliptical truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 29-44.
    3. Christian E. Galarza & Tsung-I Lin & Wan-Lun Wang & Víctor H. Lachos, 2021. "On moments of folded and truncated multivariate Student-t distributions based on recurrence relations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 825-850, August.
    4. Moshe Pollak & Michal Shauly-Aharonov, 2019. "A Double Recursion for Calculating Moments of the Truncated Normal Distribution and its Connection to Change Detection," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 889-906, September.
    5. Ogasawara, Haruhiko, 2021. "A non-recursive formula for various moments of the multivariate normal distribution with sectional truncation," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
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