Moments

Hi;

The first moment is called mean, the second is variance, the third is
skewness and the fourth is called kurtosis......What about higher
moments? Do they have specific names......

Partho

Ben wrote:

> Hi;
> 
> The first moment is called mean, the second is variance, the third is
> skewness and the fourth is called kurtosis......What about higher
> moments? Do they have specific names......
> 
> Partho
> 
Only when you've spent all day struggling with the math and still can't 
get them to be the same from one calculation to the other.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google?  See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

I don't think that skewnew is the name for the third moment or kurtosis for 
the fourth.  Skew and the kurtosis are the names for parameters of 
distributions relative to the Gaussian.

In article <1151426851.864050.130660@b68g2000cwa.googlegroups.com>, "Ben" 
<partho.choudhury@gmail.com> wrote:
>Hi;
>
>The first moment is called mean, the second is variance, the third is
>skewness and the fourth is called kurtosis......What about higher
>moments? Do they have specific names......
>
>Partho
>

I thought they applied to all distributions and not just normal ones!!!

any inputs?

Partho


John Herman wrote:
> I don't think that skewnew is the name for the third moment or kurtosis for
> the fourth.  Skew and the kurtosis are the names for parameters of
> distributions relative to the Gaussian.
>
> In article <1151426851.864050.130660@b68g2000cwa.googlegroups.com>, "Ben"
> <partho.choudhury@gmail.com> wrote:
> >Hi;
> >
> >The first moment is called mean, the second is variance, the third is
> >skewness and the fourth is called kurtosis......What about higher
> >moments? Do they have specific names......
> >
> >Partho
> >

OK I have found the answer - Plz cf

http://mathworld.wolfram.com/Skewness.html

and

http://mathworld.wolfram.com/Kurtosis.html

So obv, skewness and kurtosis apply to non-normal distributions too!!!

So now the question hangs - What about fifth and sixth and.....monents?
Do they exist and do they have specific names??

Curious!!!!

Partho



John Herman wrote:
> I don't think that skewnew is the name for the third moment or kurtosis for
> the fourth.  Skew and the kurtosis are the names for parameters of
> distributions relative to the Gaussian.
>
> In article <1151426851.864050.130660@b68g2000cwa.googlegroups.com>, "Ben"
> <partho.choudhury@gmail.com> wrote:
> >Hi;
> >
> >The first moment is called mean, the second is variance, the third is
> >skewness and the fourth is called kurtosis......What about higher
> >moments? Do they have specific names......
> >
> >Partho
> >

John Herman wrote:
> I don't think that skewnew is the name for the third moment or kurtosis for
> the fourth.  Skew and the kurtosis are the names for parameters of
> distributions relative to the Gaussian.

All those "moments" with a name aren't really moments in anycase, since
they are centered. For example, for the Cauchy distribution there
exists no variance, but a second moment (which is infinite).

Regards,
Andor


>
> In article <1151426851.864050.130660@b68g2000cwa.googlegroups.com>, "Ben"
> <partho.choudhury@gmail.com> wrote:
> >Hi;
> >
> >The first moment is called mean, the second is variance, the third is
> >skewness and the fourth is called kurtosis......What about higher
> >moments? Do they have specific names......
> >
> >Partho
> >

So are you implying that there is some fundamental difference between
nth order moments and corresponding (nth order) central moments - I
thought that the only difference between them was the use of x-m
instead of x in case of central moments.....where m=mean

Partho


Andor wrote:
> John Herman wrote:
> > I don't think that skewnew is the name for the third moment or kurtosis for
> > the fourth.  Skew and the kurtosis are the names for parameters of
> > distributions relative to the Gaussian.
>
> All those "moments" with a name aren't really moments in anycase, since
> they are centered. For example, for the Cauchy distribution there
> exists no variance, but a second moment (which is infinite).
>
> Regards,
> Andor
>
>
> >
> > In article <1151426851.864050.130660@b68g2000cwa.googlegroups.com>, "Ben"
> > <partho.choudhury@gmail.com> wrote:
> > >Hi;
> > >
> > >The first moment is called mean, the second is variance, the third is
> > >skewness and the fourth is called kurtosis......What about higher
> > >moments? Do they have specific names......
> > >
> > >Partho
> > >

Andor wrote:

> John Herman wrote:
>> I don't think that skewnew is the name for the third moment or kurtosis
>> for
>> the fourth.  Skew and the kurtosis are the names for parameters of
>> distributions relative to the Gaussian.
> 
> All those "moments" with a name aren't really moments in anycase, since
> they are centered. For example, for the Cauchy distribution there
> exists no variance, but a second moment (which is infinite).
> 

So you're saying that a second moment exists although the integral diverges?
In fact any moments mu_k, where k>=1, diverge for Cauchy distribution and
are quite often declared to be undefined.

> Regards,
> Andor
> 
> 
>>
>> In article <1151426851.864050.130660@b68g2000cwa.googlegroups.com>, "Ben"
>> <partho.choudhury@gmail.com> wrote:
>> >Hi;
>> >
>> >The first moment is called mean, the second is variance, the third is
>> >skewness and the fourth is called kurtosis......What about higher
>> >moments? Do they have specific names......
>> >
>> >Partho
>> >

-- 
Jani Huhtanen
Tampere University of Technology, Pori

Jani Huhtanen wrote:
> Andor wrote:
>
> > John Herman wrote:
> >> I don't think that skewnew is the name for the third moment or kurtosis
> >> for
> >> the fourth.  Skew and the kurtosis are the names for parameters of
> >> distributions relative to the Gaussian.
> >
> > All those "moments" with a name aren't really moments in anycase, since
> > they are centered. For example, for the Cauchy distribution there
> > exists no variance, but a second moment (which is infinite).
> >
>
> So you're saying that a second moment exists although the integral diverges?
> In fact any moments mu_k, where k>=1, diverge for Cauchy distribution and
> are quite often declared to be undefined.

The difference lies in the ability to specify a limit, even if it is
infinity. For example

limit_{x->inf} x = inf.

However,

limit_{x->inf} x sin(x)

does not exist. Check out the section "Why the second moment of the
Cauchy distribution is infinite" in

http://en.wikipedia.org/wiki/Cauchy_distribution

Regards,
Andor

Ben wrote:
> So are you implying that there is some fundamental difference between
> nth order moments and corresponding (nth order) central moments - I
> thought that the only difference between them was the use of x-m
> instead of x in case of central moments.....where m=mean

Don't know if it is fundamental, but it certainly is a difference
(noticable when the mean does not exist, for example).