A GEOMETRICAL APPROACH TO THE SPECIAL STABLE DISTRIBUTIONS.

Abstract

If X and Y are independent and normal about 0, possibly with different variances, then Z = XY/(X2 + Y2)1/2 is also normally distributed about 0. This is known and known to be tantamount to the stability of the distribution of X-2. The present paper reduces the distribution of Z to a very elementary fact of plane geometry and shows geometrically that it also implies the stability of the Cauchy distribution. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1966
Accession Number
AD0646047

Entities

People

  • L. J. Savage

Organizations

  • Yale University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Geometry
  • Mathematics
  • Plane Geometry
  • Sizes (Dimensions)

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Systems Analysis and Design