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 Post subject: I need a deciderPosted: Wed, 7 Mar 2012 06:14:44 UTC
 Senior Member

Joined: Sat, 10 Oct 2009 15:43:22 UTC
Posts: 110
I'm having a debate with my roommate.

In short my roommate stated in a statistics homework assignment that chebychev's theorem supported a claim that a particular distribution was a skewed distribution. I do not think it's possible to derive any conclusion about a distribution's graphical shape using chebychev's. Would anyone care to speculate? Thanks

MF

_________________
let:
a=b
ab=b^2
ab-a^2=b^2-a^2
a(b-a)=(b+a)(b-a)
a=b+a
a=2a
1=2

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 Post subject: Re: I need a deciderPosted: Wed, 7 Mar 2012 09:44:57 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 7622
Location: NCTS/TPE, Taiwan
mgfortes wrote:
I'm having a debate with my roommate.

In short my roommate stated in a statistics homework assignment that chebychev's theorem supported a claim that a particular distribution was a skewed distribution. I do not think it's possible to derive any conclusion about a distribution's graphical shape using chebychev's. Would anyone care to speculate? Thanks

MF

Chebyshev's inequality (one- or two-sided) doesn't tell you anything about skewness. And it is a pretty crude bound.

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 Post subject: Re: I need a deciderPosted: Wed, 7 Mar 2012 14:48:53 UTC
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Joined: Mon, 23 Jun 2003 17:34:53 UTC
Posts: 2094
Location: San Antonio,Texas USA
The usual form of Chebychev's Inequality only requires two moments of the distribution, so it is valid even if a distribution does not have higher moments. And yes, it's a crude bound because it has to work for any distribution with a finite variance.

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Live long and prosper.

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