On the existence of moments in Cauchy-like distributions induced from the tan function
DOI: 361 Downloads 7884 Views
Author(s)
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 |