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st: RE: RE: RE: A math question


From   "Rubil Ivica" <irubil@eizg.hr>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: RE: A math question
Date   Fri, 21 Dec 2012 16:55:58 +0100

CJ,
both the median and the mean are so-called "functionals" - functions of functions, the latter being (in the case of the mean and the median) the distribution function. In your case, you have a vector-valued function, where the "structure" of the vector is determined by the distribution function of abs(x^3), call it F(.). So what you need is the functional form of F(.). 

--
Ivica Rubil
Ekonomski institut || The Institute of Economics, Zagreb
Trg J. F. Kennedyja 7, 10 000 Zagreb, Croatia
tel. +385-1-2362-269 || fax. +385-1-2335-165
irubil@eizg.hr || www.eizg.hr

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of CJ Lan
Sent: 21. prosinac 2012 16:42
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: RE: A math question

Al, 

I think the "median" is a function, just like the "mean" is a function, not just a number.

BTW, the derivative of abs(x^3) should be 3*x*abs(x) because the derivative can be derived as
 abs(x^3)/(x^3)*(3*x^2) = 3*abs(x)*x^2/x = 3*x*abs(x). 

I wish others could shed a light too?  Thx.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Feiveson, Alan H. (JSC-SK311)
Sent: Friday, December 21, 2012 10:28 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: A math question

CJ -The median is one number, not a function - so it doesn't make sense to talk about differentiating it.


If you mean what is the derivative of abs(x^3) with respect to x, it would be 3*x^2, because the derivative for x < 0 is the same as for x > 0 = 3*x^2. 



Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of CJ Lan
Sent: Friday, December 21, 2012 9:13 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: A math question

Folks,

I am not sure if this is an appropriate question but I am hoping someone wh= o knows the answer do not mind rendering her/his hands.

What is the derivative of the median(abs(x^3)) with respect to x ?

Thank you.

CJ


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