The probability distribution for the ratio of variables having a normal distribution

Details

• Personal Author:
  Jones, R. M.
• Corporate Authors:
  Environmental Research Laboratories (U.S.) ; Wave Propagation Laboratory
• NOAA Program & Office:
  OAR (Oceanic and Atmospheric Research)
• Description:
  "The probability density function is derived for the ratio of two independent random variables, each of which has a normal distribution. When the variances of the normal distributions are small, a simplifying approximation to the probability density function for the ratio of the two variables is valid; the lower tail of the approximate distribution is approximately normal. This result validates the bias-correction calculation for minimum-envelope processing of skywave radar sea-echo spectra presented in a previous report. The distribution function for the ratio approaches a normal distribution as the variances for the numerator and denominator distributions approach zero, in agreement with previous, related calculations."
• Keywords:
  Distribution (Probability Theory) Echo Spectra Distribution (Probability Theory)
• Series:
  NOAA technical memorandum ERL/WPL   84
• Document Type:
  Technical Memorandum
• License:
  https://creativecommons.org/publicdomain/zero/1.0/
• Rights Information:
  CC0 Public Domain
• Compliance:
  Library
• Main Document Checksum:
  urn:sha256:e0ecb2f421a62886b44ca958414527d2628af452ffc11e7ced6162dc27a51aad
• Download URL:
  https://repository.library.noaa.gov/view/noaa/30191/noaa_30191_DS1.pdf
• File Type:
  [PDF - 2.86 MB ]