On some properties of Cauchy-Stieltjes Kernel families

Raouf Fakhfakh ()
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Raouf Fakhfakh: Jouf University

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 4, 1186-1200

Abstract: Abstract We explore properties of Cauchy-Stieltjes Kernel (CSK) families that have the same counterpart in natural exponential families (NEFs). We determine the variance function of the finite mixtures of a CSK family with its length-biased family. We also prove that, for a more natural definition for the domain of means, the new domain of means scale nicely under affine transformation.

Keywords: Mixtures of distributions; Variance function; Cauchy kernel; Domain of means; Length-biased distribution; 60E10; 46L54 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13226-021-00020-z

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