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Hypothesis testing for the generalized multivariate modified Bessel model

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  • Thabane, Lehana
  • Drekic, Steve

Abstract

In this paper, we consider hypothesis testing problems in which the involved samples are drawn from generalized multivariate modified Bessel populations. This is a much more general distribution that includes both the multivariate normal and multivariate-t distributions as special cases. We derive the distribution of the Hotelling's T2-statistic for both the one- and two-sample problems, as well as the distribution of the Scheffe's T2-statistic for the Behrens-Fisher problem. In all cases, the non-null distribution of the corresponding F-statistic follows a new distribution which we introduce as the non-central F-Bessel distribution. Some statistical properties of this distribution are studied. Furthermore, this distribution was utilized to perform some power calculations for tests of means for different models which are special cases of the generalized multivariate modified Bessel distribution, and the results compared with those obtained under the multivariate normal case. Under the null hypothesis, however, the non-central F-Bessel distribution reduces to the central F-distribution obtained under the classical normal model.

Suggested Citation

  • Thabane, Lehana & Drekic, Steve, 2003. "Hypothesis testing for the generalized multivariate modified Bessel model," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 360-374, August.
    • Handle: RePEc:eee:jmvana:v:86:y:2003:i:2:p:360-374
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    References listed on IDEAS

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    1. Barndorff-Nielsen, O. & Blæsild, P. & Halgreen, C., 1978. "First hitting time models for the generalized inverse Gaussian distribution," Stochastic Processes and their Applications, Elsevier, vol. 7(1), pages 49-54, March.
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    Cited by:

    1. Teng, Suyan & Lee, Loo Hay & Chew, Ek Peng, 2010. "Integration of indifference-zone with multi-objective computing budget allocation," European Journal of Operational Research, Elsevier, vol. 203(2), pages 419-429, June.
    2. Heinen, Andréas & Valdesogo, Alfonso, 2020. "Spearman rank correlation of the bivariate Student t and scale mixtures of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    3. Olcay Arslan, 2015. "Variance-mean mixture of the multivariate skew normal distribution," Statistical Papers, Springer, vol. 56(2), pages 353-378, May.

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