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Improving the Variability Function in Case of a Monotonic Probability Distribution

Author

Listed:
  • Sans W.

    (Institute of Applied Mathematics and Statistics, Sanderring 2, D-97070 Würzburg, Germany)

  • Zhai X.

    (Institute of Applied Mathematics and Statistics, Sanderring 2, D-97070 Würzburg, Germany)

  • Stübner D.

    (Institute of Applied Mathematics and Statistics, Sanderring 2, D-97070 Würzburg, Germany)

  • Sen S.

    (Institute of Applied Mathematics and Statistics, Sanderring 2, D-97070 Würzburg, Germany)

  • Binder A.

    (University of Applied Sciences Würzburg, Department of Computer Science, Münzstr. 9, D-97070 Würzburg, Germany)

  • Collani E. v.

    (Institute of Economics, Sanderring 2, D-97070 Würzburg, Germany)

Abstract

In [v. Collani, Theoretical Stochastics, Heldermann Verlag, 2004] the Bernoulli Space is introduced as fundamental model of uncertainty replacing Kolmogorov's probability space which though appropriate for defining a special branch of mathematics has hardly importance for describing real world. In [Stübner, Sans, Zhai, v. Collani, Economic Quality Control 19: 215-228, 2004] a general method for improving the variability function χ of a given Bernoulli Space is proposed. Subsequently this method has been applied to the case of uniform distributions in [Sans, Stübner, Sen, v. Collani, iapqr transactions 30: 2005]. In this paper the method is extended to cover the monotonic probability distributions.

Suggested Citation

  • Sans W. & Zhai X. & Stübner D. & Sen S. & Binder A. & Collani E. v., 2005. "Improving the Variability Function in Case of a Monotonic Probability Distribution," Stochastics and Quality Control, De Gruyter, vol. 20(1), pages 121-142, January.
    • Handle: RePEc:bpj:ecqcon:v:20:y:2005:i:1:p:121-142:n:2
    DOI: 10.1515/EQC.2005.121
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    References listed on IDEAS

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    1. Stübner Dmitri & Sans Wolfgang & Zhai Xiaomin & Sen Surath & von Collani Elart, 2004. "Measurement Procedures for Improving the Variability Function," Stochastics and Quality Control, De Gruyter, vol. 19(2), pages 215-228, January.
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    Cited by:

    1. Sen Surath & von Collani Elart, 2007. "A Note on the Moments of Random Variables," Stochastics and Quality Control, De Gruyter, vol. 22(2), pages 223-246, January.
    2. Schelz F. & Sans W. & v. Collani E., 2007. "Improving the Variability Function in Case of a Uni-Modal Probability Distribution," Stochastics and Quality Control, De Gruyter, vol. 22(1), pages 19-39, January.
    3. Zhai Xiaomin, 2008. "Two Old Statistical Methods in a New Stochastic Outfit," Stochastics and Quality Control, De Gruyter, vol. 23(1), pages 29-38, January.
    4. von Collani Elart, 2008. "A Critical Note on the Guide to the Expression of Uncertainty in Measurement (GUM)," Stochastics and Quality Control, De Gruyter, vol. 23(1), pages 123-149, January.

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    1. Sen Surath & von Collani Elart, 2007. "A Note on the Moments of Random Variables," Stochastics and Quality Control, De Gruyter, vol. 22(2), pages 223-246, January.
    2. Zhai Xiaomin, 2008. "Two Old Statistical Methods in a New Stochastic Outfit," Stochastics and Quality Control, De Gruyter, vol. 23(1), pages 29-38, January.

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