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A generalized multivariate beta distribution: control charting when the measurements are from an exponential distribution

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  • K. Adamski
  • S. Human
  • A. Bekker

Abstract

In Statistical Process Control (SPC) there exists a need to model the run-length distribution of a Q-chart that monitors the process mean when measurements are from an exponential distribution with an unknown parameter. To develop exact expressions for the probabilities of run-lengths the joint distribution of the charting statistics is needed. This gives rise to a new distribution that can be regarded as a generalized multivariate beta distribution. An overview of the problem statement as identified in the field of SPC is given and the newly developed generalized multivariate beta distribution is proposed. Statistical properties of this distribution are studied and the effect of the parameters of this generalized multivariate beta distribution on the correlation between two variables is also discussed. Copyright Springer-Verlag 2012

Suggested Citation

  • K. Adamski & S. Human & A. Bekker, 2012. "A generalized multivariate beta distribution: control charting when the measurements are from an exponential distribution," Statistical Papers, Springer, vol. 53(4), pages 1045-1064, November.
    • Handle: RePEc:spr:stpapr:v:53:y:2012:i:4:p:1045-1064
    DOI: 10.1007/s00362-011-0407-0
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    References listed on IDEAS

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    1. A. El-Bassiouny & M. Jones, 2009. "A bivariate F distribution with marginals on arbitrary numerator and denominator degrees of freedom, and related bivariate beta and t distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(4), pages 465-481, November.
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    Cited by:

    1. Laradji, A., 2015. "Sums of totally positive functions of order 2 and applications," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 176-180.

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