Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

Sample Means of Independent Standard Cauchy Random Variables Are Standard Cauchy: A New Approach

Michael P. Cohen
The American Mathematical Monthly
Vol. 119, No. 3 (March 2012), pp. 240-244
DOI: 10.4169/amer.math.monthly.119.03.240
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.119.03.240
Page Count: 5
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
Item Type
Article
References
Sample Means of Independent Standard Cauchy Random Variables Are Standard Cauchy: A New Approach
Preview not available

Abstract

Abstract A remarkable property of the Cauchy distribution is that the sample mean of standard Cauchy random variables itself has a standard Cauchy distribution. This result can be shown using characteristic functions, convolution integrals, or multidimensional change of variables (Jacobians). A new method of proof based on the periodicity properties of the tangent function is presented.

Page Thumbnails