Linear Combinations,Products and Ratios of Simplicial or Spherical Variates |
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| Authors: | S. Kalke F. Thauer |
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| Affiliation: | Institute of Mathematics , University of Rostock , Rostock , Germany |
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| Abstract: | The density level sets of the two types of measures under consideration are l 2, p -circles with p = 1 and p = 2, respectively. The intersection-percentage function (ipf) of such a measure reflects the percentages which the level set corresponding to the p-radius r shares for each r > 0 with a set to be measured. The geometric measure representation formulae in Richter (2009 Richter , W.-D. (2009). Continuous l n, p -symmetric distributions. Lithuanian Mathemat. J. 49:93–108.[Crossref], [Web of Science ®] , [Google Scholar]) is based upon these ipf's and will be used here for evaluating exact cdf's and pdf's for the linear combination, the product, and the ratio of the components of two-dimensional simplicial or spherically distributed random vectors. |
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| Keywords: | Cauchy distribution Density generating function Exact statistical distributions Geometric measure representation Generalized uniform distribution Intersection-percentage function Linear combinations of random variables Products of random variables Ratios of random variables Spherical distributions Simplicial distributions l 2,p -generalized arc-length measure |
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