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Inferences on the ratio of two generalized variances: independent and correlated cases

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  • Ali Jafari

Abstract

Statistical inferences about the dispersion of multivariate population are determined by generalized variance. In this article, we consider constructing a confidence interval and testing the hypotheses about the ratio of two independent generalized variances, and the ratio of two dependent generalized variances in two multivariate normal populations. In the case of independence, we first propose a computational approach and then obtain an approximate approach. In the case of dependence, we give an approach using the concepts of generalized confidence interval and generalized p value. In each case, simulation studies are performed for comparing the methods and we find satisfactory results. Practical examples are given for each approach. Copyright Springer-Verlag 2012

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  • Ali Jafari, 2012. "Inferences on the ratio of two generalized variances: independent and correlated cases," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 297-314, August.
    • Handle: RePEc:spr:stmapp:v:21:y:2012:i:3:p:297-314
    DOI: 10.1007/s10260-012-0191-6
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    1. SenGupta, Ashis, 1987. "Tests for standardized generalized variances of multivariate normal populations of possibly different dimensions," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 209-219, December.
    2. Ram Tripathi & Ramesh Gupta & John Gurland, 1994. "Estimation of parameters in the beta binomial model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 317-331, June.
    3. Sarkar, Sanat K., 1989. "On improving the shortest length confidence interval for the generalized variance," Journal of Multivariate Analysis, Elsevier, vol. 31(1), pages 136-147, October.
    4. Iliopoulos, George, 2008. "UMVU estimation of the ratio of powers of normal generalized variances under correlation," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1051-1069, July.
    5. George Iliopoulos, 2001. "Decision Theoretic Estimation of the Ratio of Variances in a Bivariate Normal Distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 436-446, September.
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    Cited by:

    1. H. Zakerzadeh & A. Jafari, 2015. "Inference on the parameters of two Weibull distributions based on record values," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 25-40, March.
    2. Dariush Najarzadeh, 2019. "Testing equality of standardized generalized variances of k multivariate normal populations with arbitrary dimensions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 593-623, December.

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