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On Some Characteristics of the Joint Distribution of Sample Variances

Author

M. Hafidz Omar, Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia  and

Anwar H. Joarder, Department of Computer Science and Engineering, Faculty of Science and Engineering, Northern University of Business and Technology Khulna, Khulna-9100, Bangladesh

The joint distribution of correlated sample variances and their product moments have been derived. Finite expressions have been derived for product moments of sample variances of integer orders. Marginal and conditional distributions, conditional moments, coefficient of skewness and kurtosis of conditional distribution of a sample variance given the other variance have also been discussed. Shannon entropy of the distribution is also derived. When the variables are uncorrelated, the resulting characteristics match with the independent case of sample variances.

Keywords: Joint Distribution of Sample Variances; Bivariate Distribution; Bivariate Normal Distribution, Correlated Chi-Square Variables; Product Moments

References:
  1. Abramowitz, M. and Stegun, I. (1964). Handbook of Mathematical Functions, Dover Publications, New York.
  2. Ahmed, S.E. (1992). Large sample pooling procedure for correlation. The Statistician, 41, 415-428.
  3. Anderson, T.W. (2003). An Introduction to Multivariate Statistical Analysis. John Wiley and Sons. New York.
  4. Fisher, R.A. (1915). Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika, 10, 507-521.
  5. Gradshteyn, I.S. and Ryzhik, I.M. (1995). Table of Integrals, Series and Products, Academic Press.
  6. Joarder, A.H. and Ahmed, S.E. (1996). Estimation of characteristic roots of scale matrix. Metrika, 44(3), 259 – 267.
  7. Joarder, A.H. (2009). Moments of the product and ratio of two correlated chi-square random variables. Statistical Papers, 50(3), 581-592.
  8. Joarder, A.H. and Abujiya, M.R. (2009). Standardized moments of bivariate chi-square distribution. Journal of Applied Statistical Science, 16(4), 1-9.
  9. Johnson, N.L., Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions (volume 1). John Wiley and Sons, New York.
  10. Krishnaiah, P.R.; Hagis, P. and Steinberg, L. (1963). A note on the bivariate chi distribution. SIAM Review, 5, 140-144.

How to Cite

MLA 9th Edition

Omar, M. Hafidz, and Anwar H. Joarder. “On Some Characteristics of the Joint Distribution of Sample Variances.” BL COLLEGE JOURNAL, vol. 4, no. 1, July 2022, pp. 126–39. https://doi.org/10.62106/blc2022v4i1e2

APA 7th Edition

Omar, M. H., & Joarder, A. H. (2022). On Some Characteristics of the Joint Distribution of Sample Variances. BL COLLEGE JOURNAL4(1), 126–139. https://doi.org/10.62106/blc2022v4i1e2

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