AP Statistics Curriculum 2007 Rice - Revision history

Tdlee: Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

2020-03-03T17:09:13Z

Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

JayZzz: /* Moments */

2011-07-18T22:52:06Z

‎Moments

JayZzz at 04:38, 7 July 2011

2011-07-07T04:38:35Z

JayZzz at 04:34, 7 July 2011

2011-07-07T04:34:15Z

JayZzz at 04:33, 7 July 2011

2011-07-07T04:33:44Z

JayZzz: Created page with '== General Advance-Placement (AP) Statistics Curriculum - Rice Distribution== ===Rice Distribution=== Also known as the Rician Distribution, t…'

2011-07-07T04:30:29Z

Created page with '== General Advance-Placement (AP) Statistics Curriculum - Rice Distribution== ===Rice Distribution=== Also known as the Rician Distribution, t…'

New page

==[[AP_Statistics_Curriculum_2007 | 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''' 
<math>\frac{x}{\sigma^2}\exp\left(\frac{-(x^2+\nu^2)}
{2\sigma^2}\right)I_0\left(\frac{x\nu}{\sigma^2}\right)</math>

'''CDF''' 
<math>1-Q_1\left(\frac{\nu}{\sigma },\frac{x}{\sigma }\right)</math>

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

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

'''Support''' 
''x'' ∈ [0, +∞)

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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

−	{{translate\|pageName=http://wiki.~~stat~~.~~ucla~~.edu~~/socr~~/index.php/AP_Statistics_Curriculum_2007_Rice}}	+	"{{translate\|pageName=http://wiki.socr.umich.edu/index.php/AP_Statistics_Curriculum_2007_Rice}}

@@ Line 21: / Line 21: @@
 ===Moments===
-The first few [[raw moments]] are:
+The first few [http://en.wikipedia.org/wiki/Raw_moment raw moments] are:
 :<math>\mu_1^'=  \sigma  \sqrt{\pi/2}\,\,L_{1/2}(-\nu^2/2\sigma^2)</math>

@@ Line 4: / Line 4: @@
 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''' <br>
+'''PDF''': <br>
 <math>\frac{x}{\sigma^2}\exp\left(\frac{-(x^2+\nu^2)}
 {2\sigma^2}\right)I_0\left(\frac{x\nu}{\sigma^2}\right)</math>
-'''CDF''' <br>
+'''CDF''': <br>
 <math>1-Q_1\left(\frac{\nu}{\sigma },\frac{x}{\sigma }\right)</math>
-'''Mean''' <br>
+'''Mean''': <br>
 <math>\sigma  \sqrt{\pi/2}\,\,L_{1/2}(-\nu^2/2\sigma^2)</math>
-'''Variance''' <br>
+'''Variance''': <br>
 <math>2\sigma^2+\nu^2-\frac{\pi\sigma^2}{2}L_{1/2}^2\left(\frac{-\nu^2}{2\sigma^2}\right)</math>
-'''Support''' <br>
+'''Support''': <br>
 ''x'' ∈ [0,&thinsp;+∞)

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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

−	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php/~~AP_Statistics_Curriculum_2007_Johnson_SB~~}}	+	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_Rice}}

← Older revision		Revision as of 04:33, 7 July 2011
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	'''Support''' <br>		'''Support''' <br>
	''x'' ∈ [0, +∞)		''x'' ∈ [0, +∞)
		+
		+	===Moments===
		+	The first few [[raw moments]] are:
		+
		+	:<math>\mu_1^'= \sigma \sqrt{\pi/2}\,\,L_{1/2}(-\nu^2/2\sigma^2)</math>
		+	:<math>\mu_2^'= 2\sigma^2+\nu^2\,</math>
		+
		+	===Applications===
		+	Describing fading in wireless communications systems analysis <br>
		+	http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1532472
		+
		+	Radar signal processing <br>
		+	http://users.ece.gatech.edu/mrichard/Rice%20power%20pdf.pdf
		+
		+	Describing noisy MRI Data <br>
		+	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
		+
		+	<hr>
		+	* SOCR Home page: http://www.socr.ucla.edu
		+
		+	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_Johnson_SB}}