Nakagami distribution information

Nakagami
	Probability density function
	Cumulative distribution function
Parameters	shape (real); spread (real)
Support
PDF
CDF
Mean
Median	No simple closed form
Mode
Variance

The Nakagami distribution or the Nakagami-m distribution is a probability distribution related to the gamma distribution. It is used to model physical phenomena, such as those found in medical ultrasound imaging, communications engineering, meteorology, hydrology, multimedia, and seismology.

The family of Nakagami distributions has two parameters: a shape parameter $m\geq 1/2$ and a second parameter controlling spread $\Omega >0$ .

Nakagami distribution information

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Nakagami
Probability density function
Cumulative distribution function
Parameters	$m{\text{ or }}\mu \geq 0.5$ shape (real) $\Omega {\text{ or }}\omega >0$ spread (real)
Support	$x>0\!$
PDF	${\frac {2m^{m}}{\Gamma (m)\Omega ^{m}}}x^{2m-1}\exp \left(-{\frac {m}{\Omega }}x^{2}\right)$
CDF	${\frac {\gamma \left(m,{\frac {m}{\Omega }}x^{2}\right)}{\Gamma (m)}}$
Mean	${\frac {\Gamma (m+{\frac {1}{2}})}{\Gamma (m)}}\left({\frac {\Omega }{m}}\right)^{1/2}$
Median	No simple closed form
Mode	$\left({\frac {(2m-1)\Omega }{2m}}\right)^{1/2}$
Variance	$\Omega \left(1-{\frac {1}{m}}\left({\frac {\Gamma (m+{\frac {1}{2}})}{\Gamma (m)}}\right)^{2}\right)$