Questions tagged [uniform]

The uniform distribution describes a random variable that is equally likely to take any value in its sample space.

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Calculating probability based on mixed variables

Assume there are $K$ people and iid. parameters $a_1,\ldots,a_K$ associated to them with $a_i \sim U(0,1)$. Person $i$ observes his own fixed $a_i$ with some noise: \begin{equation} X^{(1)}_i= a_i+ e^...
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Any practical uses of inverse uniform distribution?

To motivate a paper in game-theory I need examples of real-life uses of the inverse uniform distribution (http://en.wikipedia.org/wiki/Inverse_distribution#Inverse_uniform_distribution). Which type of ...
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Test the randomness (uniformly distributed) on a 64 bit float random generator

We have a random number generator which is supposed to generate 64 bit floats, uniformly. We want to test whether it is a good uniformly random. I am not asking the general way to test it, as it was ...
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PIT on a sample with m bins, and KS test used to estimate a good value for m

I know about PIT, but this works only when you know the distribution, or at least have a strong hint. What I am trying to achieve is to transform a given sample into an equivalent sample with ...
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What is the ratio of uniform and normal distribution?

Let $X$ follow a uniform distribution and $Y$ follow a normal distribution. What can be said about $\frac X Y$? Is there a distribution for it? I found the ratio of two normals with mean zero is ...
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Geometric mean of uniform variables

I am doing some independent study in asymptotic statistics and point estimation and am aware that you can get from log transformations of uniform random variables (exponential) all the way up to chi-...
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What probability distribution is to the discrete uniform distribution as the beta distribution is to uniform distribution over $[0,1]$?

A beta distribution with its parameters $\alpha = \beta = 1$ is the uniform $[0, 1]$ distribution. What distribution is to the discrete uniform distribution (the sample space is left undecided), as ...
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'Uniformization'?

I am looking for a better term for what I call 'uniformification', where I change data to make it more close to uniformly distributed. I am doing a project in which I try to make the output of a ...
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Expected standard deviation for a sample from a uniform distribution?

I've been trying to find information on the sampling distribution of the standard deviation for uniform distributions and have been having a heck of a time figuring out the expected value for the ...
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Help understanding uniform marginal distribution in Farlie-Morgenstern family.

http://imgur.com/FeFf3e9 The imgur link is to a screenshot of the relevant section in my text. I have trouble understanding how if $H(x, \infty)=F(x)$ is the marginal distribution of $x$, how $F(x) = ...
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Statistical test for uniform distribution

I have a sample of 5 numbers from known interval [0, 10]. Is 5 numbers is enough to make some conclusions about whether these numbers are drawn from uniform distribution or not?
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Quality of randomness in generated random number

I have generated a list of 3 random number where each summed to 1. I would like to access the quality of randomness. What is the best mechanism to access this randomness? E.g my random numbers are. ...
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Random number generation distributed like a translated weibull from uniform random generator

If $X$ is uniformly distributed on $(0,1)$, then the random variable $ \lambda(-\ln(1-X))^{1/k}\ $, is Weibull distributed with parameters $k$ and $\lambda$. With this, I can get random numbers ...
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Divergence from uniform distribution (continuous): dispersion measure?

I have data of a continuous random variable within the range [-1,1], which sometimes is concentrated around 0, while other times is concentrated toward -1 and 1, while zero is relatively ...
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What's a distribution with an abyss instead of a peak?

I am looking for a (commonly used) probability density function, which would look like a normal distribution flipped upside down. It would look like a uniform distribution with a dent in the middle. ...
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Statistics Modelling Question

Here is the situation: I want to sell my house. The price I'm getting from people who want to by my house follows i.i.d. with $X_n \sim \text{Uniform}(0,1)$, where $X_n$ is the highest offer on the $...
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How to generate random points in the volume of a sphere with uniform nearest neighbour distances

With respect to post (1) and post (2), I generated a large number of uniformly distributed points inside the ball of radius $R$ using $\frac{R_s U^{1/3}}{\sqrt{X_1^2 + X_2^2 + X_3^2}} (X_1, X_2, X_3)$,...
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Uniform updating [closed]

I have a uniform prior with certain values $a$ and $b$ (not standard uniform). How do I update this distribution to take into account the results from my data? If it was $U(0,1)$, I could convert it ...
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If ϵ is uniformly distributed, then a linear probability model is appropriate? Can I find any Literature?

A latent variable model involving a binomial observed variable $Y$ can be constructed such that $Y$ is related to the latent variable $Y^*$ via $ Y = \begin{cases} 0, & \mbox{if }Y^*...
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how calculate expected value

(Ross [2009], p.162) The current in a semiconductor diode is often measured by the Shockley equation I = I0(e^aV-1) where V is the voltage across the diode; I0 is the reverse current; a is a constant; ...
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Transforming a uniform-on-sphere random vector

Consider the 3-D real random vector $(X_1,X_2,X_3)$ which is uniformly distributed on the surface of a unit sphere. What can be told about the distribution of $(aX_1,bX_2,cX_3)$, where $a,b,c,$ are ...
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Jeffreys prior for continuous uniform distribution

A nonnegative random variable $x$ has a continuous uniform distribution in the interval $(0,\theta)$. Therefore, the likelihood is given by: $f(x|\theta) = \frac{1}{\theta}I(x\leq\theta)$, where $I$ ...
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Conditional Distribution over the unit disc

How can I show that, $U$ and $V$, two independent uniform $(-1,1)$ random variables have a conditional distribution, given that $U^2 + V^2 <1$, that takes the form: $$f_{U,V|U^2+V^2<1} (u,v|w&...
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Why is the distribution of rand()^2 different than of rand()*rand()?

In Libre Office Calc, the rand() function is available, which chooses a random value between 0 and 1 from a uniform distribution. I'm a bit rusty on my probability, ...
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Obtaining single connected component through uniform sampling in a circle

I would be really glad if someone could help me with the following problem: Let us consider a circular environment with $R=1$ and $n$ points uniformly distributed within the circle's area. All these ...
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Interarrival time distribution of uniform arrival process

I am currently trying to model an uniform arrival process within my simulation model. However, I can only model it by means of an interarrival time (I can let the model wait for a certain amount ...
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How can we find the decision boundary for two overlapping continuous uniform distribution?

Say I have $X \sim \text{CUnif}(a, b)$ and $Y \sim \text{CUnif}(c, d)$. The parameters of $X$ and $Y$ overlap i.e., $a < c < b < d$. How can I find a decision boundary in such case? I am ...
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Can we make the Irwin-Hall distribution more general?

I need to find a symmetric low-kurtosis distribution class, which includes the uniform, the triangular and the normal Gaussian distribution. The Irwin-Hall distribution (sum of standard uniform) ...
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Expected value of $Ye^X$ where $X \sim U(0,1)$ and $Y \sim U(0,1)$

I am trying to find the expected value of $Z$ where $Z = Y\cdot e^X$ where $Y \sim U(0,1)$ and $X \sim U(0,1)$. My attempt so far: $$F_Z(z) = P(Ye^X \le z) = \int \int_{Ye^X \le z} f(x,y)\, dxdy$$ ...
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Generating discrete uniform from coin flips

Suppose you have a fair coin which you can flip as many times as you want (possibly countably infinite). Is it possible to generate the discrete uniform distribution on $(1,2,...,k)$, where $k$ is NOT ...
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Obtain order statistics using uniform order statistics

This is a homework questions. Can you guys give me some hints? Let $U_{(1)}<\cdots<U_{(n)}$ be the order statistics of a sample of size $n$ from a Uniform$(0,1)$ population. Show that $F^{-1}(...
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Estimating the parameter of a uniform distribution: improper prior?

We have N samples, $X_i$, from a uniform distribution $[0,\theta]$ where $\theta$ is unknown. Estimate $\theta$ from the data. So, Bayes' rule... $f(\theta | {X_i}) = \frac{f({X_i}|\theta)f(\theta)}...
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Is variance computed on weekly basis the same as variance computed on daily basis?

I have a proportion value computed on a weekly basis with 95% confidence interval. Now I want to get the proportion on a daily basis, instead. Assuming the values are uniformly distributed, I divided ...
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Probability distribution and uniform distribution in a sphere [duplicate]

my question is related on this one that I have posed on math.stackexchange but is not exactly the same (even I would appreciate receive an answer for the other as well). Since I haven't received ...
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1answer
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Sample from continuous uniform distribution with open interval

If I want to sample from a continuous uniform distribution with interval $(a,b]$, how can I do it in R? Or is it just the same as sampling from $(a,b)$ in ...
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Should percentiles of one set of samples from a distribution wrt another set be uniformly distributed?

I'd like to pose the following question which for some reason is proving to be unclear to me. Assume we have the Normal distribution, mean 0, sd 1. Let's say we take 1000 samples from it; call them $...
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Measure for the uniformity of a distribution

I can't seem to find a well established and simple statistical measure of uniformity in occurrence datasets in the presence of zero-valued categories. I've looked at Shannon's entropy which seems to ...
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Generate pairs of random numbers uniformly distributed and correlated

I would like to generate pairs of random numbers with certain correlation. However, the usual approach of using a linear combination of two normal variables is not valid here, because a linear ...
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Why is Entropy maximised when the probability distribution is uniform?

I know that entropy is the measure of randomness of a process/variable and it can be defined as follows. for a random variable $X \in$ set $A$ :- $H(X)= \sum_{x_i \in A} -p(x_i) \log (p(x_i)) $. In ...
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Probability of getting a specific Tetris piece given previous pieces

I'm doing a small reinforcement learning project involving Tetris, just for fun. Considering that each piece has a constant probability of being selected, how can I calculate the probability of ...
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Compute expectation of a random variable given the density function

The probability density function is given by: $f(t)= (8-t)^2 /9$ for $5 \le t \le 8$ Compute the mean daily CPU time. Hence state the mean of a new variable $W=T+12$ hours. For this question, ...
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Statistics of sample correlation for uniformly distributed samples

I am computing the sample correlation between two vectors of uncorrelated and uniformly distributed samples using MATLAB. More precisely, I compute $$ r_N=\frac{1}{N}\sum_{i=1}^N x_{i}\, y_{i}, $$ ...
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What is the benefit of using permutation tests?

When testing some null versus alternative hypotheses by a test statistic $U(X)$, where $X = \{ x_i, ..., x_n\}$, apply the permutation test with the set $G$ of permutations on $X$ and we have a new ...
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“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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Uniform distribution - a simple question

I know this is a really simple one, but for some reason I see various ways and I'm not sure which one should I follow. So - I have $Y_1,...Y_n \sim U(1,3)$ and I want to know $P(y<c)$. The answer ...
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Tail bounds on Euclidean norm for uniform distribution on $\{-n,-(n-1),…,n-1,n\}^d$

What are known upper bounds on how often the Euclidean norm of a uniformly chosen element of $\:\{-n,~-(n-1),~...,~n-1,~n\}^d\:$ will be larger than a given threshold? I'm mainly interested in bounds ...
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The difference of two discrete uniform variables taken modulo. Is still uniform?

I have a uniform distribution that generates from the $\mathbb{Z}_q$ (so I have integers from the interval [$-q/2$, $q/2$). Then I subtract one from the other and take the result modulo $q$ (so again ...
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Covariance of a set of uniformly distributed unit vectors?

I have a set of uniformly distributed unit vectors within a "cone" (essentially a subset of a uniform distribution on the unit sphere, as described here). I've found how to get the covariance matrix ...
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What is the difference between two discrete uniform distribution with the same range but different number of categories?

Two random number generators with uniform distributions having min, max as (0,8) The first generates all integers between 0 and 8 uniformly. But the second generates only [0,2,4,6,8] uniformly. What ...
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458 views

Calculating confidence intervals for a proportion when there are no 'successes' in the sample

I'm looking to analyse 400k replies to a Facebook-equivalent post to determine how many of them are written by bots, and how many of them are written by real people. I don't have the resources to ...