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# 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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### Sobol variance based decomposition

I have 6 input variables, each of which is normally distributed. Can I use Sobol variance-based sensitivity analysis? I have read some articles where they said that input variables must have uniform ...
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### placing bets to maximize the difference between two random numbers

Suppose you are asked to bet on the difference between two independent randomly numbers $r_1$ and $r_2$, both uniformly distributed between 0 and 1. Your bet size is $w$ is between -1 and 1. Your ...
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### Given n uniformly distributed r.v's, what is the PDF for one r.v. divided by the sum of all n r.v's?

I'm interested in the following type of case: there are 'n' continuous random variables which must sum to 1. What then would be the PDF for any one individual such variable? So, if $n=3$, then I am ...
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### Expected number of uniform distributions

Suppose you have i.i.d uniformly distributed numbers $u_i \in [0,1], i=1,2,\dots$, which are realized sequentially. At the start of the game, $u_1$ is drawn. After you know the realization of $u_1$, ...
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### What is a good example of a non-informative prior for the uniform distribution?

I recently noticed that for non-informative priors, people usually use something like a uniform prior, which works for many different distributions. However, assuming that your likelihood is nothing ...
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### Probability and conditional distribution

I'm finding difficulties in cracking this probability problem. Let's say that we have $n$ players, who are supposed to be part of two teams, red and blue. They are divided with the following procedure....
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### Two dimensional discrete uniform distribution

I was wondering... Is there any formula for a two dimensional discrete uniform distribution? I've googled a little bit but I don't seem to find anything... I hope that somebody can help!
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### How good is my shuffling algorithm?

I've implemented an array-shuffling algorithm, and I want to prove to myself that I didn't make any mistakes in the implementation. Running it $n$ times on a small list, I can record the frequency ...
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### modeling a mixture of a Gaussian and Uniform (Matlab)

I'm trying to fit some data to a Gaussian + Uniform mixture model. This model has three parameters: the mean and standard deviation of the Gaussian, and the relative weights of the distributions (...
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### How to test if my data fits a uniform distribution with SAS?

I have a target variable with upper and lower natural limits (cannot be negative and can not be bigger than 100). Therefore, I would like to know if I could use ...
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### What's the name for a distribution of the form $10^D$, where $D$ is a known distribution?

In my particular case, I'm generating uniformly random numbers and using them as the power to a base-10 exponent, e.g. in R: s <- 10^runif(10, 1, 10) Is there ...
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### Distribution of the largest fragment of a broken stick (spacings)

Let a stick of length 1 be broken in $k+1$ fragments uniformly at random. What is the distribution of the length of the longest fragment? More formally, let $(U_1, \ldots U_k)$ be IID $U(0,1)$, and ...
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### Reasoning regarding non-informative priors

I'm not sure whether this counts as a question. However, I'd be happy to receive feedback for the validity of my reasoning. Recently, I read a bit about Jeffreys' prior and the "problem" with using ...
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### Why is the CDF of a sample uniformly distributed

I read here that given a sample $X_1,X_2,...,X_n$ from a continuous distribution with cdf $F_X$, the sample corresponding to $U_i = F_X(X_i)$ follows a standard uniform distribution. I have ...
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### How to compute and interpret the confidence interval on a QQ plot [duplicate]

I often see QQ-plots with a confidence interval: For my application, I have a QQ plot of test p-values against a uniform distribution. I want to add the 95% CI of the observed p-values on the plot, ...
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### Probabilities of conditional expectation values in uniform distribution

Let's consider a continuous random variable $X$ as follows: $f_X(x)=\left\{ \begin{array}{ll}\frac{1}{2}, &\mbox{if} \ x\in[0,1] \\ \frac{1}{4}, &\mbox{if}\ x\in(1,3]\end{array}\right.$ ...
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### Translating and scaling a uniform discrete distribution?

Is it possible to map a uniform, discrete distribution over two integers $A$, $B$ (lower and upper bounds respectively) onto $[A^*, B^*]$ while keeping the distribution discrete uniform? We may assume ...
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### KS test for Uniformity

I am attempting to use the KS-test to test whether a set of points is uniformly distributed over an interval, and I had a question about whether there may be a more optimal test for what I'm trying to ...
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### Testing whether sampling (convex polytope) is uniform

Currently, I am sampling points from: i) a convex polytope (i.e. Ax <= b) ii) a high dimensional simplex The algorithms I am using are hit-and-run and a simple version of Bayesian bootstrap. I ...
I am looking at the answer on this thread: Why likelihood is not always a density function? Here as I understand that the likelihood function is given by: $$L(\theta) = \frac{1}{\theta} \quad \... 1answer 405 views ### How to find points uniformly distributed from another point on an n-sphere? I have a point, P on an n-sphere (n=300) and I want to sample from a uniform distribution of points a given distance, d, from P. This distance is not critical. For example, if my sphere was the globe ... 1answer 962 views ### Conditional mass function of minimum of two discrete uniform random variables given the maximum I'm revising for an upcoming exam with old assignment questions, but I got this one wrong at the time and we aren't given model solutions. Looking for advice on whether or not my second attempt for A) ... 0answers 32 views ### Cumulative distribution functions (cdfs) range uniformly [duplicate] I am confused .. how does this happen? "continuous cumulative distribution functions (cdfs) range uniformly over the open interval (0,1).". How does the cdf range "uniformly" (each value having the ... 0answers 72 views ### How to derive an estimator for the parameter of a continuous uniform distribution X_1, X_2,\dots.,X_n are i.i.d. random variates drawn from a continuous uniform distribution over [0,\theta]. The sufficient statistic is denoted \max. I want an estimator e of \theta that ... 1answer 9k views ### What does log-uniformly distribution mean? When someone say a data is sampled from a log-uniformly distribution between 128 and 4000, what does that mean? How that different to sampling from a uniformly distribution? See this paper: http://... 0answers 36 views ### German tank variant: estimate resolution of camera given cropped photo sizes Make whatever assumptions you like, but I like the flavor of nonparametric techniques. I have a list of the x_i by y_i resolutions of a number of photos, all cropped from photos taken at the same ... 1answer 1k views ### Non-uniform distribution of p-values when simulating binomial tests under the null hypothesis I heard that under the null hypothesis the p-value distribution should be uniform. However, simulations of binomial test in MATLAB return very different-from-uniform distributions with mean larger ... 0answers 115 views ### Derivation of Olsens LS Selectivity Correction There are many estimation procedures that correct for sample selection. The most famous is Heckman's two-step selectivity correction (in two equations) that assumes bivariate normality of the error ... 1answer 1k views ### A question about a sum of squares of uniform random variables For independent and identical V_1,V_2\in U(-1,1), what is the probability that V_1^2+V_2^2<1? I tried but can't get an answer, the answer is \frac{\pi}{4} 1answer 54 views ### Uniform with dependent parameters I was helping a student with a question I couldn't solve. We have the following process: X is sampled from a U(0,1) distribution. Then Y is sampled from a U(-x,x) distribution. Therefore I have Y|... 0answers 41 views ### Why small values produce undulating densities when ploting logarithm of a loguniform prior (in R)? I am using a program that draws random values in a log-uniform distribution let say between 1 and 100. When I plot the density of the produced values with R it looks like a log-uniform distribution ... 0answers 64 views ### Estimator of The Mean of the Ratio of Uniformly Distributed Variables Given two random variables,  X \sim U \left[ {\mu}_{x} - \frac{{l}_{x}}{2} > 0, {\mu}_{x} + \frac{{l}_{x}}{2} \right]  and  Y \sim U \left[ {\mu}_{y} - \frac{{l}_{y}}{2} > 0, {\mu}_{y} + \... 1answer 378 views ### Joint PDF of a Uniform Distribution The Question I have a sample X1,...,Xn i.i.d. drawn from a uniform distribution unif[0,\theta], θ ∈ Θ = R+; And I'd just like to compute the joint PDF The Solution I have the following solution ... 2answers 170 views ### Return value of uniform distributions for MCMC simulations I am confused about how what value should be returned from a uniform distribution when using MCMC simulations. The proper normal distribution is define as$$ p(\theta) = \left\{ \begin{array}{cc} 1/...
This is a direct continuation of my recent question. The thing that I actually want to get is the distribution of $a+d+\sqrt{(a-d)^2+4bc}$, where $a,b,c,d$ are uniform in $[0,1]$. Now, the ...