A new confidence interval for standardized generalized variances of k-multivariate normal populations

References

• Anderson, T. W. 2003. An introduction to multivariate statistical analysis. 3rd ed. Wiley Series in Probability and Statistics. Hoboken, NJ: Wiley.
   Google Scholar
• Beals, R., and J. Szmigielski. 2013. Meijer G-functions: A gentle introduction. Notices of the American Mathematical Society 60 (6):866–72. doi:10.1090/noti1016.
   Google Scholar
• Cohen, A. 1972. Improved confidence intervals for the variance of a normal distribution. Journal of the American Statistical Association 67 (338):382–7. doi:10.1080/01621459.1972.10482394.
   Google Scholar
• Djauhari, M. 2009. Asymptotic distribution of sample covariance determinant. MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics 25:79–85.
   Google Scholar
• Djauhari, M. A. 2005. Improved monitoring of multivariate process variability. Journal of Quality Technology 37 (1):32–9. doi:10.1080/00224065.2005.11980298.
   Web of Science ®Google Scholar
• Djauhari, M. A., M. Mashuri, and D. E. Herwindiati. 2008. Multivariate process variability monitoring. Communications in Statistics – Theory and Methods 37 (11):1742–54. doi:10.1080/03610920701826286.
   Web of Science ®Google Scholar
• Hamed, M. S. 2014. Generalized variance chart for multivariate quality control process procedure with application. Applied Mathematical Sciences 8 (163):8137–51. doi:10.12988/ams.2014.49734.
   Google Scholar
• Hoel, P. G. 1937. A significance test for component analysis. The Annals of Mathematical Statistics 8 (3):149–58. doi:10.1214/aoms/1177732411.
   Google Scholar
• Iliopoulos, G., and S. Kourouklis. 1998. On improved interval estimation for the generalized variance. Journal of Statistical Planning and Inference 66 (2):305–20. doi:10.1016/S0378-3758(97)00090-6.
   Web of Science ®Google Scholar
• Jafari, A. A. 2012. Inferences on the ratio of two generalized variances: Independent and correlated cases. Statistical Methods & Applications 21 (3):297–314. doi:10.1007/s10260-012-0191-6.
   Web of Science ®Google Scholar
• Jafari, A. A., and M. R. Kazemi. 2014. Inferences on the generalized variance under normality. Journal of the Iranian Statistical Society 13 (1):57–67.
   Google Scholar
• Mathai, A. M., and R. K. Saxena. 1973. Generalized hypergeometric functions with applications in statistics and physical sciences. Lecture Notes in Mathematics. Heidelberg: Springer.
   Google Scholar
• Mathai, A. M., and P. G. Moschopoulos. 1992. A form of multivariate gamma distribution. Annals of the Institute of Statistical Mathematics 44 (1):97–106. doi:10.1007/BF00048672.
   Web of Science ®Google Scholar
• Nagata, Y. 1989. Improvements of interval estimations for the variance and the ratio of two variances. Journal of the Japan Statistical Society, Japanese Issue 19 (2):151–61.
   Google Scholar
• Najarzadeh, D. 2017. Testing equality of generalized variances of k multivariate normal populations. Communications in Statistics – Simulation and Computation 46 (8):6414–23. doi:10.1080/03610918.2016.1204457.
   Web of Science ®Google Scholar
• Najarzadeh, D. 2019a. Confidence intervals for product of powers of the generalized variances of k multivariate normal populations. Communications in Statistics – Simulation and Computation 48 (4):1264–76. doi:10.1080/03610918.2017.1410711.
   Web of Science ®Google Scholar
• Najarzadeh, D. 2019b. Testing equality of standardized generalized variances of k multivariate normal populations with arbitrary dimensions. Statistical Methods & Applications 28 (4):593–623. doi:10.1007/s10260-019-00456-y.
   Web of Science ®Google Scholar
• Noor, A. M., and M. A. Djauhari. 2010. Monitoring the variability of beltline moulding process using Wilks’s statistic. Malaysian Journal of Fundamental and Applied Sciences 6 (2):116–20.
   Google Scholar
• Peña, D., and J. Rodrı́guez. 2003. Descriptive measures of multivariate scatter and linear dependence. Journal of Multivariate Analysis 85 (2):361–74. doi:10.1016/S0047-259X(02)00061-1.
   Web of Science ®Google Scholar
• Pham-Gia, T., and N. Turkkan. 2010. Exact expression of the density of the sample generalized variance and applications. Statistical Papers 51 (4):931–45. doi:10.1007/s00362-008-0187-3.
   Web of Science ®Google Scholar
• Sarkar, S. K. 1989. On improving the shortest length confidence interval for the generalized variance. Journal of Multivariate Analysis 31 (1):136–47. doi:10.1016/0047-259X(89)90056-0.
   Web of Science ®Google Scholar
• Sarkar, S. K. 1991. Stein-type improvements of confidence intervals for the generalized variance. Annals of the Institute of Statistical Mathematics 43 (2):369–75. doi:10.1007/BF00118642.
   Web of Science ®Google Scholar
• SenGupta, A. 1987a. Generalizations of Bartlett's and Hartley's tests of homogeneity using overall variability. Communications in Statistics – Theory and Methods 16 (4):987–96. doi:10.1080/03610928708829417.
   Web of Science ®Google Scholar
• SenGupta, A. 1987b. Tests for standardized generalized variances of multivariate normal populations of possibly different dimensions. Journal of Multivariate Analysis 23 (2):209–19. doi:10.1016/0047-259X(87)90153-9.
   Web of Science ®Google Scholar
• Shorrock, G. 1990. Improved confidence intervals for a normal variance. The Annals of Statistics 18 (2):972–80. doi:10.1214/aos/1176347636.
   Web of Science ®Google Scholar
• Steyn, H. S. 1978. On approximations for the central and noncentral distribution of the generalized variance. Journal of the American Statistical Association 73 (363):670–5. doi:10.1080/01621459.1978.10480076.
   Web of Science ®Google Scholar
• Tate, R. F., and G. W. Klett. 1959. Optimal confidence intervals for the variance of a normal distribution. Journal of the American Statistical Association 54 (287):674–82. doi:10.1080/01621459.1959.10501528.
   Web of Science ®Google Scholar
• Wilks, S. S. 1932. Certain generalizations in the analysis of variance. Biometrika 24 (3–4):471–94. doi:10.1093/biomet/24.3-4.471.
   Google Scholar