Questions tagged [rayleigh]

A non-negative continuous probability distribution characterized by one strictly positive parameter.

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57 views

How are the Rayleigh Distribution and Weibull Distribution related?

I am trying to work out a physically intuitive way of understanding how the Weibull arises. Also according to the Wikipedia entry on the Weibull distribution, there is some how a relation to the ...
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The log transformation of a Rayleigh distribution, or identifying the following distributions

I have a set of data which is recorded in a $\log_{10}$ scale. To be exact it is $dBV_{pk} = 20\log_{10}(V_{pk})$ units. If I plot the distribution of the logged data as a PDF I get the following: If ...
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1answer
51 views

Let $X\sim\text{Rayleigh}(\theta^{2})$. Prove that $T_{n}$ is consistent, given that $T_{n}(\textbf{X}) = \frac{1}{2n}\sum_{i=1}^{n}x^{2}_{i}$

Let $X\sim\text{Rayleigh}(\theta^{2})$. Prove that $T_{n}$ is consistent, given that $$T_{n}(\textbf{X}) = \frac{1}{2n}\sum_{i=1}^{n}x^{2}_{i}$$ MY ATTEMPT To begin with, let us notice that \begin{...
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129 views

Find maximum likelihood given Rayleigh probability function

Problem Suppose we use a Gaussian PDF to express the likelihood of light intensity prevalent on Clear, Cloudy, and Eclipse weather. The probability of a certain amount of light value (positive or ...
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585 views

Median of Rayleigh Distribution

I am not sure how to solve the following problem: The probability density function of the Rayleigh distribution is, $\ f(x;α) = \frac{x}{α^2} e^\frac{-x^2}{2α^2}, x ≥ 0, $ where α is the scale ...
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1answer
98 views

Relating Means/Stds Between Gaussian and Rayleigh Distributions

Suppose I have something like a targeting problem, where I specify an angular dispersion in the up and down direction with two Gaussian distributions, each having a mean of 0 and a std of 0.3 degrees. ...
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238 views

Finding the parameters of a (possibly) Rayleigh distributed data set

An object is tracked in an experiment I ran. The object's velocities over a 100 time steps are recorded. A model for this object says the velocities should be Rayleigh distributed. Question 1: For ...
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1answer
105 views

Conditional distribution of multivariate Rayleigh distribution

The correlated Rayleigh envelopes using a set of zero-mean complex Gaussian RVs (Random Variables) is given by $$G_{k}=\sigma_{k}(\sqrt{1-\lambda_k^2}X_k+\lambda_kX_0)+i\sigma_{k}(\sqrt{1-\lambda_k^2}...
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128 views

Finding mean and variance of $Y = \ln{\left(\sum_i X_{i}^{2}\right)}$ for $X_i \sim \mathrm{Rayleigh}(\sigma)$

For some set of $n$ i.i.d. variables $\{X \}$ which are Rayleigh-distributed such that $$ P(X|\sigma) = \frac{X}{\sigma^2}\exp{\left[-\frac{X^2}{2\sigma^2}\right]} $$ I'm interested in anything we ...
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Assess whether the generated data follows the distribution

Using the Inverse function method I managed to draw a sample of 500 random data from a Cumulative distribution function. $f(x)$,$F(x)$ and $F_X^{-1}(u)$ are as follows: $$f_X=\frac{x}{5}exp\left({\...
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827 views

Using a Random number Generator to draw samples from a Cumulative Distribution function

I am given a Rayleigh, distribution function:$$f(x)=\frac{1}{5}x\exp\left(\frac{-x^2}{10}\right)$$ with $x>0$ and asked to: Use an appropriate random number generator algorithm to draw 500 samples ...
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175 views

Rayleigh Distribution Quartiles

The Rayleigh distribution has PDF f(x) =xe−$\frac{x^2}{2}$, x >0. Let X have the Rayleigh distribution. (a) Find P(1< X < 3).(b) Find the first quartile, median, and third quartile of X. ...
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186 views

Intuition for Rayleigh PDF

We have ground-truth data $\mathbf{x}^* = (0,0)^T \in \mathbb{R}^{2}$. Furthermore, we have $N$ measurements $\mathbf{x}_i \in \mathbb{R}^{2}, i\in \{1,\ldots,N\}$. We calculate the $N$ error vectors $...
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Can deviance residuals from a Rayleigh distribution be negative?

I'm fitting a nonlinear dynamic model to some non-normally distributed data using maximum likelihood estimation. My working approach has been to assume my data is gamma distributed and do gamma ...
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1answer
455 views

How can I transform a Rayleigh distribution to Standard Normal space?

I need to transform a function of Rayleigh distributed variates $G(X)$ to one in standard normal space $G(U)$. The transformation is governed by equal exceedance probabilities in both spaces, such ...
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1answer
845 views

Parameter estimation of a Rayleigh random variable with an offset

I have data that is believed to be Rayleigh distributed (according to some academic papers). However, when I plot the histogram (probability normalized below) it looks like a Rayleigh distribution ...
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1answer
393 views

Estimating R90 (radius of a circle expected to include 90% of impacts)

I want to determine how big a target I can hit with a bow at a certain distance with 90% probability. I place some paper targets at that distance and shoot 20 arrows at them. I have a ruler and a ...
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240 views

Distribution of the sample mean of a Rayleigh random variable

Let $\{X_1,X_2,X_3\ldots,X_n\}$ be a random sample from a Rayleigh distribution with shape parameter $b$. Let $\bar{X}=(1/n)\sum_{i=1}^nX_i$ denote the sample mean. QUESTION 1: What is the ...
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2k views

Variance of the maximum likelihood estimator of Rayleigh Distribution

I want to calculate the variance of the maximum likelihood estimator of a Rayleigh distribution using $N$ observations. The density probability function of this distribution is : $$ f(\sigma,y_i) = \...
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Testing if points on a line are over/under dispersed

I have a series of about 1000 points on a chromosome and I want to know if they are clumped, over-dispersed, or neither. The chromosome can be viewed as a 1-dimensional. I've looked over some ...
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1answer
754 views

Plain english explanation of the Rayleigh distribution?

I need to understand the Rayleigh distribution for a homework assignment in computer networks. Unfortunately, I lack the background knowledge in the field of statistics and probability theory to ...
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498 views

Distribution of distance from center of sample group

We have a bivariate normal process where $X, Y \sim N(0, \sigma)$, with no covariance. (For convenience we can assert that $\sigma = 1$, or that we have a good estimate for its value.) What is the ...
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Is it possible to convert a Rayleigh distribution into a Gaussian distribution?

...and how might we do this? If possible, I am curious if outliers in the Rayleigh distributed data would also remain outliers in the new Gaussian distributed data. Thanks.
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Sampling distribution of the radius of 2D normal distribution

The bivariate normal distribution with mean $\mu$ and covariance matrix $\Sigma$ can be re-written in polar coordinates with radius $r$ and angle $\theta$. My question is: What is the sampling ...
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135 views

Distribution of Extreme Spread for n, sigma

Simple form provided by WHuber: What is the distribution of the diameter of n points in the plane drawn iid from a bivariate Normal distribution? (Diameter is the greatest distance among any pair of ...
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2answers
318 views

Estimating variance of center-censored Normal samples

I have normally-distributed processes from which I get small samples (n typically 10-30) that I want to use to estimate variance. But frequently the samples are so close together that we can't ...
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1answer
669 views

“Convert” Rayleigh random variable into a Uniform random variable?

I have a nested question of sorts. My first question, is that I am wondering if it is possible to 'convert' a Rayleigh random variable into a uniform random variable, and how one may do this. ...
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3k views

Derivation of Rayleigh-distributed random variable

I only have a uniform distribution function between [0,1]. And from this distribution, I should generate a sequence of Rayleigh distributed random variable using some software. Anyhow, I was able to ...