# Questions tagged [rayleigh]

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

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### 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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### 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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### 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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### 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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### 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. ...
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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### 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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### 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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### 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 ...
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 ...