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PostPosted: Thu, 3 May 2012 20:50:01 UTC 
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Hi everyone! I'm having a lot of issues with this question. I have a bunch of data points and I want to prove that it came from an exponential distribution. Is the expected value for each category just 1/"sigma"? I did not receive a value for "sigma" - is that 1/the mean?

I am trying hard to find good examples to refer to, but am running into roadblocks.

Thank you so much.


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PostPosted: Thu, 3 May 2012 21:56:59 UTC 
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Usual terminology "sigma" is root mean square (square root of centralized second moment {variance}).


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PostPosted: Thu, 3 May 2012 21:58:01 UTC 
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jasper wrote:
Hi everyone! I'm having a lot of issues with this question. I have a bunch of data points and I want to prove that it came from an exponential distribution. Is the expected value for each category just 1/"sigma"? I did not receive a value for "sigma" - is that 1/the mean?

I am trying hard to find good examples to refer to, but am running into roadblocks.

Thank you so much.


\sigma is the standard deviation.

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PostPosted: Thu, 3 May 2012 22:20:22 UTC 
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Gah! I'm so sorry, I feel stupid now. I didn't mean "sigma," I think I meant gamma.

So according to this --http://www.aiaccess.net/English/Glossaries/GlosMod/e_gm_exponential.htm -- mu is equal to one over gamma. So would that mean the expected value of each frequency would be the same, one over mu?


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PostPosted: Fri, 4 May 2012 11:46:15 UTC 
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Asssuming frequentist interpretation, just test goodness of fit as with any other distributions.

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\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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