Communications for Statistical Applications and Methods

  • 제21권1호
  • /
  • Pages.81-91
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  • 2014
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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A Note on the Characteristic Function of Multivariate t Distribution

  • 투고 : 2013.10.31
  • 심사 : 2013.12.18
  • 발행 : 2014.01.31
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초록

This study derives the characteristic functions of (multivariate/generalized) t distributions without contour integration. We extended Hursts method (1995) to (multivariate/generalized) t distributions based on the principle of randomization and mixtures. The derivation methods are relatively straightforward and are appropriate for graduate level statistics theory courses.

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참고문헌

  1. Abramowitz, M. and Stegun, I. A. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, INC, New York.
  2. Arellano-Valle, R. B. and Bolfarine, H. (1995). On some characterizations of the t distribution, Statistics & Probability Letters, 25, 79-85. https://doi.org/10.1016/0167-7152(94)00208-P
  3. Barndorff-Nielsen, O. (1978). Hyperbolic distributions and distributions on hyperbola, Scandinavian Journal of Statistics, 5, 151-157.
  4. Barndorff-Nielsen, O. and Blaesild, P. (1981). Hyperbolic distributions and ramifications: Contributions to theory and application, In Taillie, C., Patil, G. P. and Baldessari, B. A., editors, Statistical Distributions in Scientific Work, 4, 19-44, D. Reidel Publishing Company, Dordrecht.
  5. Barndorff-Nielsen, O., Kent, J. and Sorensen, M. (1982). Normal variance-mean mixtures and z distribution, International Statistical Review, 50, 145-159. https://doi.org/10.2307/1402598
  6. Datta, G. S. and Ghosh, M. (2007). Characteristic functions without contour integration, The American Statistician, 61, 67-70. https://doi.org/10.1198/000313007X170422
  7. Dreier, I. and Kotz, S. (2002). A note on the characteristic function of the t-distribution, Statistics & Probability Letters, 57, 221-224. https://doi.org/10.1016/S0167-7152(02)00032-9
  8. Durrett, R. (1996). Probability: Theory and Examples, 2nd edition, Duxbury Press, New York.
  9. Fang, K. T., Kotz, S. and Ng, K. W. (1990). Symmetric Multivariate and Related Distributions, Chapman and Hall, London.
  10. Feller, W. (1966). An Introduction to Probability Theory and Its Applications, Volume II, Wiley, New York.
  11. Fisher, R. A. and Healy, M. J. R. (1956). New tables of Behrens' test of significance, Journal of Royal Statistical Society B, 18, 212-216.
  12. Hurst, S. (1995). The characteristic function of the student t distribution, Financial Mathematic Re-search Report 006-95, Australian National University, Canberra ACT 0200, Australia.
  13. Ifram, A. F. (1970). On the characteristic function of F and t distributions, Sankhya A, 32, 350-352.
  14. Kotz, S. and Nadarajah, S. (2004). Multivariate t Distributions and Their Applications, Cambridge University Press, Cambridge.
  15. Pestana, D. (1977). Note on a paper by Ifram, Sankhya Series A, 39, 396-397.
  16. Sutradhar, B. C. (1986). On the characteristic function of multivariate Student t-distribution, Canadian Journal of Statistics, 14, 329-337. https://doi.org/10.2307/3315191
  17. Sutradhar, B. C. (1988). Author's revision on the characteristic function of multivariate Student t-distribution, Canadian Journal of Statistics, 16, 323. https://doi.org/10.2307/3314742
  18. Watson, G. N. (1966). A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge.