# Questions tagged [rayleigh-distribution]

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

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### I can't decide if this is a rayleigh or poisson distribution

So here is the distribution it are certain events of time spent behind your telephone. I just can't decide which distribution it follows. I have thought about Poisson or Rayleigh.
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### Statistical test for comparing directional data

I have a dataset with number of bats flying out in 8 directions from their home site (i.e) I studied a bat colony with N individuals and I have counted the number of bats (from that colony) that flew ...
1answer
38 views

### How to insert a normal distribution into another function?

I am struggling with the following problem. TLDR: I want to merge the uncertainty of the normal distribution into another function. Imagine a certain significant wave height (Hs) of 2 metres in a sea ...
0answers
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### Confidence Limits for normal vs rayleigh distributed random variables

I have a device to measure a coordinate in one axis, the measurement error is $\Delta x$, which is specified that $3\sigma < thr$, where thr is say 1 nanometer, and the average is not specified. ...
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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 ...
1answer
647 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 ...
1answer
1k 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 ...
1answer
581 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 ...
0answers
263 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 ...
2answers
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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47 views

### 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 ...
1answer
919 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 ...
1answer
724 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 ...
2answers
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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.
1answer
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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 ...
1answer
140 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 ...
2answers
347 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 ...
1answer
798 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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### 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 ...