Questions tagged [rayleigh-distribution]

Question 1

Given two random variables $X \sim N(0, \sigma_X^2)$, $Y \sim N(0, \sigma_Y^2)$ and $R = \sqrt{X^2 + Y^2}$, I'm trying to circularise the distribution of $R$ for further comparison against other less ...

Question 2

I am working with Rayleigh and Exponential random variables. These have convenient closed form confidence intervals for their parameter estimator. But now we are interested in making a statement of ...

Question 3

The method-of-moment of $\sigma$ for the following pdf is $$ \text{pdf}(x,\sigma) = \frac{x}{\sigma^2}\exp(-\frac{1}{2}\frac{x^2}{\sigma^2}) $$ $$ E[x] = \int_{0}^{\infty}\frac{x^2}{\sigma^2}\exp(-\...

Question 4

I've read on the internet that the pdf of the sample max, $X$, from among $N$ i.i.d. samples from a distribution with pdf $f(x)$ and cdf $F(x)$ is given by $$ p(X) = N f(x) F(x)^{N-1}. $$ I'm ...

Question 5

Given samples from two Rayleigh-distributed random variables with unknown parameters, $X \sim R(\sigma_x), Y \sim R(\sigma_y)$, what tests can we use to determine if and to what extent their ...

Question 6

I am looking at covering circles for cartesian coordinates given by independent bivariate random variables $X, Y \sim N(0, \sigma)$. The radius of a circle that will cover proportion p of these ...

Question 7

In short, I am looking to estimate the distribution of $ \eta = \sum_{i=1}^N (X_i - z_i)^2$, for each $X_i \sim \text{Rayleigh}(1)$ and constants $z_i$. If $X_i$ were Gaussian, then this could be ...

Question 8

Summary: If we have an unbiased MLE $\widehat{\sigma_1}$ of an exponential distribution parameter, and the confidence intervals for its estimates are given by the $\chi^2$ distribution; and we find ...

Question 9

Given an even number of sample points in a plane, I want to compute the sum of squared distances from the sample center as part of estimating the Rayleigh parameter. One way of doing it is to compute ...

Question 10

Let $X \sim \mathcal{N}\left(\mu, \Sigma \right)$, and let $A$ be a symmetric matrix. My understanding is that the Rayleigh quotient of vector $X$ is given by: $$R=\frac{X^T A X}{X^T X}$$ I've been ...

Question 11

I have a small data set which (a) is always positive and (b) is showing a right tail on the histogram. I wondered if it could be log-normal and tested for this, but to no avail. I am now wondering ...

Question 12

I have the following model. $$ z(k) = a(k) e^{i \psi(k)} + n(k)$$ The distribution of $a$ is known to be a Rayleigh and $\psi$ is known to be uniformly distributed. The noise $n$ is a white Gaussian ...

Question 13

I came across a received signal-to-interference-plus-noise-ratio (SINR), $S$, of a wireless communication system as \begin{align*} S = \frac{\phi|h|^2\rho_1}{1+|g|^{2} \rho _{2} }, \tag{1} \end{align*...

Question 14

I am trying to find what is the distribution of the ratio of two independent Rayleigh random variables, each of which has different standard deviation.

Question 15

Suppose we have two independent, uncorrelated random variables $X\sim N\left(0,a^2\right)$ and $Y\sim N\left(0,b^2\right)$ (i.e. $X$ and $Y$ are Normally distributed with mean 0 and standard ...

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Questions tagged [rayleigh-distribution]

Rayleigh Approximation of Elliptical Bivariate Gaussian Distribution Predicted vs. Empirical Discrepancy

Prediction Interval for Rayleigh or Exponential parameter estimate

Method-of-moment of n IID random variables

Sampling the max among $N$ samples from the Rayleigh distribution

Hypothesis tests for Rayleigh variables

Bivariate normal covering circles and ellipses

CDF for squared sum of Rayleigh random variables

Adjusting confidence interval of estimator by efficiency

Computing sum squared distances without computing center

Expected value of Rayleigh quotient, non-centered Gaussian vector

What is a good technique for testing whether data is Rayleigh distributed?

Estimation of parameters in case of a rayleigh random variable corrupted with Gaussian Noise

How to derive the solution of $F_S(x)=P \left ({|h|^{2} \le \frac { x \left ({1 + |g|^{2} \rho _{2} }\right)}{\phi \rho _{1}} }\right)$?

What is the distribution of the ratio of two independent variables, each subject to Rayleigh distribution with different standard deviation?

Rayleigh distribution with unequal variances

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