Is the logarithmic transformation monotonic?

Article View: sci.math.stat

Article #575

#575

From: mikef
Date: Thu, 12 Nov 1992 04:58

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I have needed to make comparisons between variances of some
random variable X, var(X). Specifically, I needed to know if 
var(X=a)>var(X=b). However, I was only able to compute var(lnX), 
and have made the comparison between var(ln{X=a}) and var(ln{X=b}).

I thought that this comparison would be valid since: 

(1) I believed the natural logarithm was a monotonic tranformation, and

(2) because, if (1) is true I thought that it then follows that
var(X=a)>var(X=b) implies that var(ln{X=a})>var(ln{X=b}).

Am I correct? If not, any good suggestions?

Thanks in advance.  


-- 
__
Michael Fahey         | Internet: mikef@pub.health.su.oz.au
Dept of Public Health | UUCP: uunet!munnari.oz.au!pub.health.su!mikef
University of Sydney  | Bitnet: mikef%pub.health.su.oz.au@cunyvm.bitnet

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Newsgroups: sci.math.stat
Path: arc1-ca.pugleaf.net!sparky!uunet!europa.asd.contel.com!darwin.sura.net!spool.mu.edu!uwm.edu!rpi!batcomputer!munnari.oz.au!metro!dph1!mikef
From: mikef@dph1.health.su.OZ.AU
Subject: Is the logarithmic transformation monotonic?
Message-ID: <1992Nov12.045820.4074@ucc.su.OZ.AU>
Followup-To: poster
Summary: Question re the nature of the log transformation
Originator: mikef@dph1
Keywords: monotonic transformation, logarithm
Sender: news@ucc.su.OZ.AU
Nntp-Posting-Host: dph1.health.su.oz.au
Organization: Dept Public Health, Sydney University
Date: Thu, 12 Nov 1992 04:58:20 GMT
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