AP Statistics Curriculum 2007 Rice

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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, +∞)