Statistical Analysis Stack Exchange
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Questions tagged [nakagami-distribution]

A two-parameter distribution, the square root of a gamma distribution. Also known as the Nakagami-m distribution.

Note that in connecting a gamma distributed X to its Nakagami distributed square root, we need to transform the distribution parameters. See Wikipedia.

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What kind of distribution does this have?

Currently I'm trying to figure out the distribution of the following: $X \sim \frac{\sqrt{n}}{\sqrt{Gamma(n,\beta)}}$ where the denominator follows a $Gamma(n,\beta)$ distribution. I've checked out these links: Square root of an inverse gamma…
BonnieKlein
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When is distribution of $|X+Y|^2 $ equivalent to $|X|^2+|Y|^2$?

I am trying to compute the distribution of the following $$Z=\bigl(X+Y\bigl)^2$$ BUT I have that both $X$ and $Y$ are Nakagami with parameter $m$. (A Nakagami random variable is the square root of a Gamma random variable.) So the above is hard to…
Tyrone
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pdf of the square of the sum of Nakagami random variables

I am trying to find the probability distribution function (pdf) of the following $$Y=\big|\sum_i X_i\big|^2=\big|\sum_{i\leq 2} h_i \, a_i\big|^2 $$ with $$h_i\sim \text{iid} \operatorname{Nakagami}(m=3,1/3)$$ $$a_i \,\text{positive constants}…
Tyrone
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What is the mean of this exponential random variable?

I have read a paper that says that the following is exponentially distributed $$ Y= \bigl| \sum_{i=1}^n \gamma_i^{-\frac{1}{2}} h_i \bigl|^2$$ where $\gamma_i$ are non-negative constants and $$h_i \sim \mathcal{CN} (0,1)\,,$$ where…
Tyrone
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product of two probability density functions

I have on one hand a z variable following a standard normal distribution N(0,1) and on the other hand a variable X following a Nakagami distribution. I am supposed to find a Gaussian distribution when I take the product of the two distributions…
NafNaf
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What is the distribution of these functions of Nakagami random variables?

I am new to this forum and hope I can get help. A Nakagami random variable $X$ with parameter $m$ has the following pdf $$X\sim \frac{2m^m}{\Gamma(m)\Omega^m} x^{2m-1}e^{-\frac{m}{\Omega}x^2}$$ Define $$ T:=|X|^2$$ 1- Is T a normalized Gamma…
Tyrone
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