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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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1answer
641 views

Prove that sum of uniform distribution (-1,1) is also uniform (-n,n)? [duplicate]

If $d_i \in U(-1,1)$ (uniform distribution between -1 and 1 - not sure what the canonical notation is for this), then it seems intuitive that $\sum_{i=1}^n d_i \in U(-n,n)$ and thus $$P\big(\sum_{i=1}^...
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1answer
948 views

Relationship between probability distribution and correlation [closed]

I'm unsure of the precise relationship between a probability distribution and correlation, in particular autocorrelation. What exactly is an autocorrelated probability distribution? It seems like ...
1
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1answer
4k views

chi-squared with too many degrees of freedom

I have a third party random number generator with a period approximately greater than $63*(2^{63} - 1)$ which generates numbers in the range $[0,2^{32}-1]$, ie $2^{32}$ different numbers. I've made ...
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1answer
31 views

Test for RVs with known probabilities?

I have written code that generates a sequence of distinct integers. The integers are assumed to occur in the sequence with fixed probabilities. For example, if the sequence contains the numbers [-1,0,...
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0answers
444 views

Empirical multivariate probability integral transform

Is there a 'simple' way to obtain a non-parametric empirical multivariate probability integral transform? Univariate case The probability integral transform relates to the transform of any random ...
5
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2answers
199 views

Estimation derived from ignorance

Is something wrong with the following reasoning? Mostly I wonder how could one derive uniformly random arrival from ignorance. But even if that derivation is invalid generally, it seems reasonable ...
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2answers
1k views

How to generate samples uniformly at random from multiple discrete variables subject to constraints?

I would like to generate a Monte Carlo process to fill an urn with N balls of I colors, C[i]. Each color C[i] has a minimum and maximum number of balls which should be placed in the urn. For ...
4
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0answers
3k views

Fisher information for uniform distribution [closed]

If I want to compute the CRLB for iid uniform on $[0,\theta]$. I need in the denominator this expression: $E_\theta\left[\left(\frac{\partial \log f(X)}{\partial \theta}\right)^2\right]=nE_\theta\left[...
8
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1answer
938 views

Correlation coefficient for a uniform distribution on an ellipse

I am currently reading a paper that claims that the correlation coefficient for a uniform distribution on the interior of an ellipse $$f_{X,Y} (x,y) = \begin{cases}\text{constant} & \text{if} \ (...
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1answer
429 views

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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0answers
273 views

approximate a probability distribution by moment matching

I have a 60-40 weighted distribution, of uniform(0,7.5) and uniform(7.5,10) respectively, i.e. $$f_X(x)=(0.6/7.5)1_{x∈[0,7.5)}+(0.4/2.5)1_{x∈[7.5,1]}$$ I have worked out that $$E(X) = 0.6(7.5/2) + ...
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1answer
146 views

Expected Values in a Uniform Distribution

I have to calculate the following: $$ E[a^{1/2}+b^{1/2}] $$ where $a=b=\frac{1}{2}\times10^{i}j$. We have that $i$ is uniformly distributed on say the $[0,1]$ interval and $j$ is also uniformly ...
2
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1answer
1k views

About calculating log-likelihood with zeroes

I would like to use the maximum log-likelihood method to find which continuous uniform distribution with the parameters $a$ and $b$ fits best to some observed data values $(x_{0}, \dots, x_{n})$. I ...
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1answer
903 views

Measure the uniformity of a distribution over weekdays

I have a similar problem to the question asked here: How does one measure the non-uniformity of a distribution? I have a set of probability distributions over the days of the week. I want to measure ...
2
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1answer
74 views

Finding the characteristic function of $Y \sim U(-1,1)$

I know that $\phi_Y(t) = E(e^{itY})=E(\cos(tY))+iE(\sin(tY))$ After integration I have found that $E(\cos(tY))= \frac{\sin(t)}{t}$ and $E(\sin(tY))=0$. So is the characteristic function just $\frac{\...
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1answer
537 views

Variance of a continuous uniformly distributed random variable

I would like to calculate the variance of a uniformly distributed continuous random variable. The probability density function of a uniformly distributed continuous random variable is $$f_{X}(x) = \...
0
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1answer
63 views

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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4answers
528 views

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 ...
2
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1answer
95 views

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 $u_1$, ...
3
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1answer
919 views

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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1answer
131 views

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....
2
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1answer
855 views

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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0answers
50 views

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 ...
1
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1answer
2k views

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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2answers
2k views

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 ...
2
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2answers
50 views

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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3answers
1k views

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 ...
2
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1answer
120 views

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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2answers
17k views

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 ...
9
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1answer
3k views

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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1answer
255 views

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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2answers
799 views

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 ...
4
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1answer
2k views

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 ...
5
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1answer
80 views

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 ...
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0answers
72 views

Question about the calculation of likelihood function [duplicate]

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 \...
1
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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 ...
6
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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) ...
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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 ...
3
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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 ...
10
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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://...
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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 ...
17
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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 ...
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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 ...
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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 $\frac{\pi}{4}$
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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|...
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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 ...
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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} + \...
4
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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 ...
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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/...
8
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2answers
278 views

PDF of a sum of dependent variables

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 ...