Improving the Variability Function in Case of a Monotonic Probability Distribution

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.