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On a Correlated Variance Ratio Distribution and Its Industrial Application

Author

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  • M. Hafidz Omar
  • Anwar H. Joarder
  • Muhammad Riaz

Abstract

The distribution of correlated variance ratio arises if variables in the parent population are correlated. One such case arises if sample observations follow independent bivariate normal distributions. We study its cumulative distribution function, raw moments, mean centered moments, coefficient of skewness and kurtosis, median and reliability. The density function is also graphed. We address the issue of the invariance of the distribution of correlated variance ratio, and testing equality of variances under correlation. Finally we exhibit an application of the said distribution in quality control problems for monitoring process outputs using control charts.

Suggested Citation

  • M. Hafidz Omar & Anwar H. Joarder & Muhammad Riaz, 2015. "On a Correlated Variance Ratio Distribution and Its Industrial Application," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(2), pages 261-274, January.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:2:p:261-274
    DOI: 10.1080/03610926.2012.735324
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    Cited by:

    1. Ogasawara, Haruhiko, 2023. "The density of the sample correlations under elliptical symmetry with or without the truncated variance-ratio," Journal of Multivariate Analysis, Elsevier, vol. 195(C).

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