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+ ...
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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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42 views

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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2answers
167 views

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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24 views

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 ...
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59 views

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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149 views

'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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110 views

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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1answer
28 views

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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1answer
84 views

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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1answer
33 views

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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1answer
65 views

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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1answer
27 views

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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1answer
58 views

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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18 views

How to capture a dataset characteristic?

I am working on microaggregation problem, where all records are clustered in groups of a minimum size. We must optimize the sum of the squared error (SSE). As I run my algorithm on forest and ...
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1answer
230 views

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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148 views

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, ...
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25 views

Uniform updating

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 $U(1,1)$, I could convert it ...
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1answer
103 views

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 ...
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83 views

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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26 views

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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1answer
122 views

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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1answer
74 views

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} ...
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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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1answer
46 views

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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66 views

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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2answers
158 views

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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152 views

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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202 views

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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35 views

posterior of uniform distribution. I keep getting 1, but that is not right

Suppose 100 animals are classified five ways: $y = (50, 10, 25, 15)$ with corresponding probabilities $(\frac{\theta_1 + \theta_2}{5}, \frac{4(1 - \theta_1)}{5}, \frac{1-\theta_2}{5}, ...
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25 views

Proving the Accept-Reject Algorithm

Prove the following is equivalent to the Accept - Reject (AR) algorithm. Generate $X \sim g$; Generate $U|X = x \sim U_{[0; Mg(x)]}$; Accept $Y = X$ if $U \le f(x)$ Return to 1. otherwise. ...
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1answer
76 views

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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64 views

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 ...
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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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117 views

Uniformly Most Powerful (UMP) test for Uniform(t,t+1)

Suppose $X_1,...,X_n$ follow a $U(t,t+1)$ distribution. Show that the UMP level alpha test for testing $H_0:t<=t^*$ vs $H_1:t>t^*$ has form: Reject $H_0$ if and only if ...
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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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109 views

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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60 views

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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18 views

If $n$ order stats are iid from Uniform(0,1), why does dividing by the highest order stat give $n-1$ order stats iid from Uniform(0,1)? [duplicate]

As the title states: If $P_{(1)}, ... ,P_{(n)}$ are order statistics of $n$ independent uniform $(0,1)$ random variables, why are $P_{(1)}/P_{(n)} ..... P_{(n-1)}/P_{(n)}$ also order statistics of ...
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1answer
122 views

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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1answer
982 views

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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1answer
151 views

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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127 views

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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1answer
89 views

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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245 views

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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1answer
122 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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1answer
91 views

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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100 views

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 ...