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Text File  |  1992-11-11  |  1.4 KB  |  38 lines
  1. Newsgroups: sci.math.stat
  2. Path: sparky!uunet!europa.asd.contel.com!darwin.sura.net!spool.mu.edu!uwm.edu!rpi!batcomputer!munnari.oz.au!metro!dph1!mikef
  3. From: mikef@dph1.health.su.OZ.AU
  4. Subject: Is the logarithmic transformation monotonic?
  5. Message-ID: <1992Nov12.045820.4074@ucc.su.OZ.AU>
  6. Followup-To: poster
  7. Summary: Question re the nature of the log transformation
  8. Originator: mikef@dph1
  9. Keywords: monotonic transformation, logarithm
  10. Sender: news@ucc.su.OZ.AU
  11. Nntp-Posting-Host: dph1.health.su.oz.au
  12. Organization: Dept Public Health, Sydney University
  13. Date: Thu, 12 Nov 1992 04:58:20 GMT
  14. Lines: 22
  15.  
  16. I have needed to make comparisons between variances of some
  17. random variable X, var(X). Specifically, I needed to know if 
  18. var(X=a)>var(X=b). However, I was only able to compute var(lnX), 
  19. and have made the comparison between var(ln{X=a}) and var(ln{X=b}).
  20.  
  21. I thought that this comparison would be valid since: 
  22.  
  23. (1) I believed the natural logarithm was a monotonic tranformation, and
  24.  
  25. (2) because, if (1) is true I thought that it then follows that
  26. var(X=a)>var(X=b) implies that var(ln{X=a})>var(ln{X=b}).
  27.  
  28. Am I correct? If not, any good suggestions?
  29.  
  30. Thanks in advance.  
  31.  
  32.  
  33. -- 
  34. __
  35. Michael Fahey         | Internet: mikef@pub.health.su.oz.au
  36. Dept of Public Health | UUCP: uunet!munnari.oz.au!pub.health.su!mikef
  37. University of Sydney  | Bitnet: mikef%pub.health.su.oz.au@cunyvm.bitnet
  38.