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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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Adjusting Uniform Probability Distribution

I'm looking for a way to adjust the probability distribution of a uniform random function I'm using in a program. I want to find some discrete probability distribution that includes a parameter for "...
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Sufficient statistics, MLE and unbiased estimators of uniform type distribution

Let $X_1, \dots, X_n$ denote a random sample of size n from the probability distribution with pdf: $$ f_X(x|\theta_1, \theta_2) = \frac{1}{\theta_2 - \theta_1} \ I(x)_{[\theta_1,\theta_2]} \ I(\...
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Uniform distribution on 255 from text [closed]

I'm trying to create a way to link letters from a text to a position between 1 to 255. For example, the text is : "stackexchange" I would like to link every letter to a number between 1 and 255. The ...
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How do I test for a symmetric distribution? [duplicate]

I collect numbers from generators that yield different ranges of whole numbers with an unknown distribution. I want to estimate the mean of the numbers outputted by this generator. I'm convinced the ...
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Determine density of $\min(X,Y)$ and $\max(X,Y)$ for independently uniform distributed variables

Two independent random variables, $X$ and $Y$, are uniformly distributed on the unit interval $(-1,1)$. Determine the density for $U=\min(X,Y)$ and for $W=\max(X,Y)$
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Drawing floating numbers with [0, 1] from uniform distribution by using numpy

I'm currently trying to draw floating numbers from a uniform distribution. The Numpy provides numpy.random.uniform. ...
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What is $EY$, if $Y=max(X_{1},X_{2},…,X_{n})$ where $X_{i}$ are observations from uniform distribution over $(0,a)$

What is $EY$, if $Y=max(X_{1},X_{2},...,X_{n})$ where $X_{i}$ are observations from uniform distribution over set $(0,a)$, $EY$ goes to $a$ as $n$ goes to infinity ?
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Limits of integration for computing a marginal distribution

I have two functions $f_x$ = $\frac{1}{2}\delta(x-5) + 1/4$ where the 1/4 corresponds to a uniform distribution from 5 to 7. I also have $f_{y|x}$ = $\frac {1}{2}\delta(y-x-4) + 1/4$ which is 1/4 in ...
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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 ...
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Defining the “uniformity” of a dataset

I am working on a few algorithms where I have a list of $N$ samples. Currently I have plotted these into a histogram and have a view of how uniform the values are distributed within an interval, which ...
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How to compute the distribution of a function of multiple random variables?

$X$ and $Y \sim U(0,1)$. Let $$\eqalign{ g(x,y) &= x &\text{ if } &x^2+y^2 \le 1 \\ &=2 &\text{ if } &x^2+y^2 \gt 1 }$$ and $Z = g(X,Y)$. How to find $F_Z(z), \...
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Distribution of transformation

Suppose $X_1,\ldots,X_n$ are i.i.d. $\mathcal U(0,1)$. I am looking for the asymptotic distribution of $$T_n = \prod_{i=1}^n [e{X_i}]^{1/\sqrt{n}} \>.$$
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Determining maximum of a noisy waveform with known frequency over multiple periods

I have a base signal which is a wave with (fairly) consistent shape and known frequency. On top of that signal is some uniformly distributed additive noise (wave goes from -1 to 1, noise is uniformly ...
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Multi-information of a uniformly distributed random variable on the L1 sphere

I posted this question in the stackexchange mathematics forum without any reponse. Maybe it was the wrong forum, so I try it here. I tried to compute the multi-information (MI) $I[\mathbf U] = \sum_{...
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Why would predicted values be normally-distributed when the actual values are uniform?

I'm building a supervised learning model where the target variable is a uniformly-distributed continuous value ranging from 0-1 (originally a rank value from 1-38000, then scaled down to 0-1). The 20 ...
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258 views

Probability of a random variable to be the largest among others

Let us have $N$ random variables generated by uniform distribution. That is, $$u_i \sim \mathcal{U}(0,1),\quad i=1,\ldots,N$$. What is the probability of $u_N$ being the largest? I.e., how can I ...
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Random Balls in Random Buckets: What are the characteristics of the distribution?

I have N buckets, numbered 1 to N. I draw k random integers, uniformly distributed in the range 1 to N, with replacement, and for each integer I drop a ball into the corresponding bucket. k can be ...
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1answer
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Integral of a conditional uniform distribution leads to improper integral

I have two uniforms distributions, $X_1 \sim\it{U}(a,b)$ and $X_2\sim\it{U}(X_1+\delta,b+\delta)$. I would like to compute $P(X_2\in[a+\delta,b+\delta])$. So I do this: $$\begin{eqnarray*} P(X_2\in[a+...
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Consider the sum of $n$ uniform distributions on $[0,1]$, or $Z_n$. Why does the cusp in the PDF of $Z_n$ disappear for $n \geq 3$?

I've been wondering about this one for a while; I find it a little weird how abruptly it happens. Basically, why do we need just three uniforms for $Z_n$ to smooth out like it does? And why does the ...
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Sample/Filter nonuniformly distributed values so that result follows a uniform distribution

I have a dataset with a nonuniform distribution. I want to sample it so that the result is uniformly distributed. If I know the class of the example, with what probability should I choose it to get a ...
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Fake uniform random numbers: More evenly distributed than true uniform data

I'm looking for a way to generate random numbers that appear to be uniform distributed -- and every test will show them to be uniform -- except that they are more evenly distributed than true uniform ...
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Probability model question [closed]

Counts of the number of broken bones in college athletes during the season would be best represented by which of the following probability models? Question options: Binomial --Thinking this is the ...
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Weak Convergence

Here is the problem (not homework), Let $U_1,\cdots,U_n$ be i.i.d. uniform$(-n,n)$ random variables. For $-n<a<b<n$, we set $1_{U_i}(a,b)$ be the indicator function such that $1_{U_i}=1$ if ...
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Sampling subsegments from discrete input ranges

I have an set of input ranges {[a1, b1], [a2, b2], ...}. Each a and b represent integer ...
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1answer
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Show that Y/Z does not have finite expectation

The unit interval (0, 1) is divided into two sub-intervals by picking a point at random from inside the interval. Denoting by Y and Z the lengths of the longer and the shorter sub-intervals ...
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Generate three correlated uniformly-distributed random variables

Suppose we have $$X_1 \sim \textrm{unif}(n,0,1),$$ $$X_2 \sim \textrm{unif}(n,0,1),$$ where $\textrm{unif}(n,0,1)$ is uniform random sample of size n, and $$Y=X_1,$$ $$Z = 0.4 X_1 + \sqrt{1 - 0.4}...
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How to test uniformity in several dimensions?

Testing for uniformity is something common, however I wonder what are the methods to do it for a multidimensional cloud of points.
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Estimated distribution of eigenvalues for i.i.d. (uniform or normal) data

Assuming I have a data set with $d$ dimensions (e.g. $d=20$) so that each dimension is i.i.d. $X_i \sim U[0;1]$ (alternatively, each dimension $X_i \sim \mathcal N[0;1]$) and independent of each other....
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What is the expectation of a normal random variable divided by uniform random variable?

I have two random variables: $x = N(0, \sigma^2)$ and $y =U[0, b]$. I need to compute $E(x/(1+y))$. How does one go about doing this? They are independent so the joint pdf is just the product of ...
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Curve smoothing in the presence of non-gaussian uncertainty

What options are available for smoothing 2-dimensional real data for which the the ordinate points are real intervals of the form $(x_j , [y_{j0} , y_{j1}])$ In my case, the data is vague because of ...
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Uniform distribution & generation of extreme values in R

I'd like to generate a new point which should be uniformly distributed on the interval [a, b) (i.e. including the left extreme value - a and exluding the right extreme value - b). The ...
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How to uniformly project a hash to a fixed number of buckets

Hi Fellow Statisticians, I have a source generating hashes (e.g. computing a string with a timestamp and other information and hashing with md5) and I want to project it into a fixed number of ...
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What is cov(X,Y), where X=min(U,V) and Y=max(U,V) for independent uniform(0,1) variables U and V?

Let $X=\min(U,V)$ and $Y=\max(U,V)$ for independent uniform(0,1) variables $U$ and $V$. What's the covariance of $X$ and $Y$? Could you develop some calculations, especially regarding the computation ...
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How does one measure the non-uniformity of a distribution?

I'm trying to come up with a metric for measuring non-uniformity of a distribution for an experiment I'm running. I have a random variable that should be uniformly distributed in most cases, and I'd ...
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1answer
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How to use ppoints to generate points within 0 and 0.05 for qq plotting in R?

I ran Tassel3 and I filtered results with p-value not more than 0.05. This way, it is ok to draw a Manhattan plot. However, for a QQ-plot there is a problem. Say I have 40 thousands SNPs, after ...
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840 views

Marginal of a uniform distribution

Given $f\left(x|\theta\right)=1/\theta, 0\leq x\leq \theta,L\left(\theta, a\right)=\left(a-\theta\right)^2,$ and $\pi\left(\theta\right)=\theta e^{-\theta},\theta\gt 0$ I've seen Problem calculating ...
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Covariance matrix of uniform spherical distribution

I need to figure out the covariance matrix of a uniform spherical distribution. But there I can't even find a closed form of the distribution. This link says it is $\frac{1}{n}\mathbf{I}$, where $\...
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1answer
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Expected value of min X for bernoulli success?

I take a SRS sample of size n from a population of x values ranging from 1 to N. Each selected unit also has a probability p of success or q = 1-p of failure (i.e. the probability of success/failure ...
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What is the probability that the $k$th element falls in a specific interval?

The question I'm referring to comes from Stack Overflow: https://stackoverflow.com/questions/8723652/estimating-number-of-results-in-google-app-engine-query In short: With $N$ ordered samples of a ...
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Determining sample size for uniform distribution

May you help me to decide what is the minimal sample size for a uniform distributed sample. Assume that I've find the sample average, standard deviation and the $\alpha$.
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Problems with extremum of two uniform random variables

Here is the problem from the book: Let $X = \min(U,V)$ and $Y = \max(U,V)$ for independent $\text{uniform}(0,1)$ variables $U$ and $V$. Find the distributions of a) $X$; b) $1-Y$; c) $Y-X$. I ...
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Kolmogorv Smirnov Test in R

I want to proof the "Relative Age Effect" of a football team. I have a list of birth dates of the team members (about 20 numbers between 1 and 365, the day of the year). I now want to use the KS-Test ...
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Generating random matrices with specific equality constraints

Suppose I want to generate a nonnegative $n \times n$ matrix $\mathbf A$ for an odd $n$ (say, $n=5$ for a good enough example), such that the individual elements are drawn from a uniform distribution ...
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How to compute $\mathbb P( 3 X_{(1)} \geq X_{(2)}+X_{(3)})$ for order statistics of a uniform distribution?

I am trying to solve a problem for my thesis and I don't see how to do it. I have 4 observations randomly taken from a uniform $(0,1)$ distribution. I want to compute the probability that $3 X_{(1)}\...
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How can I sample from a log transformed distribution using uniform distribution?

I am transforming an unscaled density function to log scale to avoid underflow issues. BI was performing integration on this function on a grid of values before I used the log transormation, to ...
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1answer
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Estimating upper bound of uniform distribution from max of sample

This is actually part of a problem from All of Statistics: $X_1, X_2, \ldots, X_n \sim \text{Uniform}(0, \Theta)$. And $Y = \text{Max}\{X_1,\ldots, X_n\}$. If you're given that $Y > c$, can you ...
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Mean and variance of a normally distributed random number created from the average of a set of uniformly distributed random numbers

An old-fashioned way of generating normally distributed random numbers entailed setting each normally distributed random number equal to the average of a set of uniformly distributed random numbers, ...
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Distribution of a ratio of uniforms: What is wrong?

Suppose that $X$ and $Y$ are two i.i.d. uniform random variables on the interval $[0,1]$ Let $Z=X/Y$, I am finding the cdf of $Z$, i.e. $ \Pr(Z\leq z) $. Now, I came up with two ways of doing this. ...
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Generating random samples from a custom distribution

I am trying to generate random samples from a custom pdf using R. My pdf is: $$f_{X}(x) = \frac{3}{2} (1-x^2), 0 \le x \le 1$$ I generated uniform samples and then tried to transform it to my custom ...
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Why are p-values uniformly distributed under the null hypothesis?

Recently, I have found in a paper by Klammer, et al. a statement that p-values should be uniformly distributed. I believe the authors, but cannot understand why it is so. Klammer, A. A., Park, C. Y.,...