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Computer algebra application to the distribution of sample correlation coefficient

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  • Nakagawa, Shigekazu
  • Niki, Naoto
  • Hashiguchi, Hiroki

Abstract

Let r be the sample correlation coefficient. In this paper, we clarify the role of computer algebra to obtain an asymptotic expansion for probability integrals of r. A key technique is to use a change of bases of the module of symmetric polynomials. We describe an algorithm for accomplishing it. We derive the asymptotic cumulants of r in terms of population cumulants. An approximate distribution of r is also given.

Suggested Citation

  • Nakagawa, Shigekazu & Niki, Naoto & Hashiguchi, Hiroki, 1998. "Computer algebra application to the distribution of sample correlation coefficient," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 45(1), pages 23-32.
    • Handle: RePEc:eee:matcom:v:45:y:1998:i:1:p:23-32
    DOI: 10.1016/S0378-4754(97)00083-9
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    References listed on IDEAS

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    1. Berkane, Maia & Bentler, P. M., 1986. "Moments of elliptically distributed random variates," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 333-335, October.
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