On the existence of moments in Cauchy-like distributions induced from the tan function

Volume 4, Issue 1, February 2019     |     PP. 1-4      |     PDF (207 K)    |     Pub. Date: March 23, 2019
DOI:    361 Downloads     7925 Views  

Author(s)

Peter Kopanov, Department of Mathematics and Informatics, Plovdiv University "Paisii Hilendarski", 4000, Plovdiv, Bulgaria
Miroslav Marinov, St Catherine's College, Oxford University, OX1 3UJ, Oxford, United Kingdom
Atakan Salimov, Technical University of Soa, Faculty of Computer systems and Technologies

Abstract
In this paper we consider cases of the existence of the moments of functions of random variables supported on a bounded interval. Our attention is restricted to the tan function, as a generalization of the Cauchy distribution which is infact the result of applying this function to a uniformly distributed variable.

Keywords
Cauchy distributions, tan function, moments

Cite this paper
Peter Kopanov, Miroslav Marinov, Atakan Salimov, On the existence of moments in Cauchy-like distributions induced from the tan function , SCIREA Journal of Mathematics. Volume 4, Issue 1, February 2019 | PP. 1-4.

References

[ 1 ] Stoyanov, J., Counterexamples in Probability, Third Edition, Dover Publications, Inc., (2013).
[ 2 ] Laha, R. G., An example of a nonnormal distribution where the quotient follows the Cauchy law. Proc. Nat. Acad. Sci. USA 44, (1958) 222-223
[ 3 ] Pitman, E. J. G. and Williams, E. G., Cauchy-distributed functions of Cauchy variates. AMS 38, (1967) 916918
[ 4 ] N. L. Johnson; S. Kotz; N. Balakrishnan, Continuous Univariate Distributions, Volume 1. New York: Wiley., (1994), Chapter 16.
[ 5 ] Feller, William, An Introduction to Probability Theory and Its Applications, Volume II (2 ed.). New York: John Wiley & Sons Inc., (1971), p. 704