AP Statistics Curriculum 2007 Rice

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'''Support''' <br>
'''Support''' <br>
''x'' ∈ [0,&thinsp;+∞)
''x'' ∈ [0,&thinsp;+∞)
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 +
===Moments===
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The first few [[raw moments]] are:
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:<math>\mu_1^'=  \sigma  \sqrt{\pi/2}\,\,L_{1/2}(-\nu^2/2\sigma^2)</math>
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:<math>\mu_2^'= 2\sigma^2+\nu^2\,</math>
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===Applications===
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Describing fading in wireless communications systems analysis <br>
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http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1532472
 +
 +
Radar signal processing <br>
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http://users.ece.gatech.edu/mrichard/Rice%20power%20pdf.pdf
 +
 +
Describing noisy MRI Data <br>
 +
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2254141/
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===SOCR Links===
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http://www.distributome.org/ -> SOCR -> Distributions -> Rice Distribution
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http://www.distributome.org/ -> SOCR -> Functors -> Rice Distribution
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http://www.distributome.org/ -> SOCR -> Modeler -> Rice_Fit Modeler
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SOCR Rice Distribution Calculator: http://socr.ucla.edu/htmls/dist/Rice_Distribution.html
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<hr>
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* SOCR Home page: http://www.socr.ucla.edu
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{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_Johnson_SB}}

Revision as of 04:25, 7 July 2011

Contents

General Advance-Placement (AP) Statistics Curriculum - Rice Distribution

Rice Distribution

Also known as the Rician Distribution, the Rice distribution is the probability distribution of the absolute value of a Circular Bivariate Normal random variable with potentially non-zero mean.

PDF
\frac{x}{\sigma^2}\exp\left(\frac{-(x^2+\nu^2)}
{2\sigma^2}\right)I_0\left(\frac{x\nu}{\sigma^2}\right)

CDF
1-Q_1\left(\frac{\nu}{\sigma },\frac{x}{\sigma }\right)

Mean
\sigma  \sqrt{\pi/2}\,\,L_{1/2}(-\nu^2/2\sigma^2)

Variance
2\sigma^2+\nu^2-\frac{\pi\sigma^2}{2}L_{1/2}^2\left(\frac{-\nu^2}{2\sigma^2}\right)

Support
x ∈ [0, +∞)

Moments

The first few raw moments are:

\mu_1^'=  \sigma  \sqrt{\pi/2}\,\,L_{1/2}(-\nu^2/2\sigma^2)
\mu_2^'= 2\sigma^2+\nu^2\,

Applications

Describing fading in wireless communications systems analysis
http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1532472

Radar signal processing
http://users.ece.gatech.edu/mrichard/Rice%20power%20pdf.pdf

Describing noisy MRI Data
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2254141/

SOCR Links

http://www.distributome.org/ -> SOCR -> Distributions -> Rice Distribution

http://www.distributome.org/ -> SOCR -> Functors -> Rice Distribution

http://www.distributome.org/ -> SOCR -> Modeler -> Rice_Fit Modeler

SOCR Rice Distribution Calculator: http://socr.ucla.edu/htmls/dist/Rice_Distribution.html




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