The uniform distribution describes a random variable that is equally likely to take any value in its sample space. A discrete random variable that is uniformly distributed on a set of outcome $\{1, 2, ..., k\}$ has probability mass function $P(X=x) = 1/k$. The continuous uniform distribution on ...
1
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2answers
37 views
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 ...
1
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1answer
42 views
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 ...
0
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2answers
70 views
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 ...
1
vote
1answer
52 views
Calculating confidence intervals for a proportion when there are no 'successes' in the sample
Newbie here! Apologies in advance if I'm asking something that is based on flawed understanding of statistical analysis.
I'm looking to analyse 400k replies to a Facebook-equivalent post, to ...
1
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1answer
90 views
How to write a function to generate a sequence of points in R?
This is the PDF that I am dealing with:
...
1
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0answers
87 views
Finding Expected Value of a discrete uniform random variable
I am stuck on a problem for my Statistical theory class.
So the problem goes like this:
Let X be the discrete uniform random variable, namely, X has the pmf:
$f(x)=\frac{1}{\theta}, ...
1
vote
2answers
43 views
Stats test which test of the NULL that a distribution is uniformally distributed
I'm looking for a statistical test which tells the probability that a given sample comes from a uniform distribution.
Shapiro test wether a sample comes from a normal distribution. I'm looking a ...
0
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0answers
28 views
Sample changing distribution
I have the following process:
I have N buckets in front of me, $M$ of which are filled with water (the other ones are empty).
I pick one of them (consider uniform distribution) and empty it (so ...
2
votes
2answers
98 views
Last-digit test and probability
I have done a last-digit test on a draw of numbers between 1 og 370. Team A drew 64 numbers from the pool, and the last digit of those numbers spread out like this:
Digit: 0 1 2 3 4 5 6 7 8 9
...
6
votes
2answers
248 views
How to find the expected distance between two uniformly distributed points?
If I were to define the coordinates $(X_{1},Y_{1})$ and $(X_{2},Y_{2})$ where
$$X_{1},X_{2} \sim \text{Unif}(0,30)\text{ and }Y_{1},Y_{2} \sim \text{Unif}(0,40).$$
How would I find the expected ...
0
votes
0answers
81 views
Uniform Random on $(-\infty,\infty)$
Imagine picking a 1 when any real number is equally likely. What is the pdf? Does this idea have a known use? What is its name?
There could be a use for a uniform random real number. It could end ...
1
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1answer
55 views
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 ...
3
votes
2answers
134 views
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]} \ ...
-3
votes
2answers
68 views
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 ...
4
votes
1answer
108 views
How do I test for a symmetric distribution?
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 ...
1
vote
2answers
409 views
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)
0
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0answers
68 views
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.
...
-1
votes
1answer
102 views
How to calculate parameters of uniform distribution from data [closed]
Let's assume the distribution of student scores in SAT exams is uniform with support [a, b]. I have information about how one group of students did in one exam: (1) 10 students scored less than 1, (2) ...
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votes
1answer
56 views
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 ?
1
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1answer
123 views
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 ...
2
votes
1answer
201 views
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 ...
1
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2answers
85 views
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 ...
3
votes
1answer
101 views
$X$ and $Y \sim U(0,1)$; by letting $Z=g(X,Y)$, how to derive $F_Z(z), E(Z)$ and $E(Z | X^2+X^2 > 1 )$
$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
}$$
and $Z = g(X,Y)$. How to find $F_Z(z), ...
0
votes
0answers
38 views
Distribution of transformation
Suppose $X_1,\ldots,X_n$ are i.i.d. $\mathcal U(0,1)$. I am looking for the asymptotic distribution of $$T_n = \prod_{i=1}^n [e{X_i}]^{1/\sqrt{n}} \>.$$
0
votes
0answers
20 views
Determining maximum of a noisy waveform with known frequency over multiple periods
I have a base signal which is a wave with (fairly) consistent shape and known frequency. On top of that signal is some uniformly distributed additive noise (wave goes from -1 to 1, noise is uniformly ...
2
votes
0answers
47 views
Multi-information of a uniformly distributed random variable on the L1 sphere
I posted this question in the stackexchange mathematics forum without any reponse. Maybe it was the wrong forum, so I try it here.
I tried to compute the multi-information (MI) $I[\mathbf U] = ...
3
votes
1answer
152 views
Why would predicted values be normally-distributed when the actual values are uniform?
I'm building a supervised learning model where the target variable is a uniformly-distributed continuous value ranging from 0-1 (originally a rank value from 1-38000, then scaled down to 0-1). The 20 ...
2
votes
2answers
105 views
Probability of a random variable to be the largest among others
Let us have $N$ random variables generated by uniform distribution. That is, $$u_i \sim \mathcal{U}(0,1),\quad i=1,\ldots,N$$.
What is the probability of $u_N$ being the largest? I.e., how can I ...
5
votes
1answer
124 views
Random Balls in Random Buckets: What are the characteristics of the distribution?
I have N buckets, numbered 1 to N.
I draw k random integers, uniformly distributed in the range 1 to N, with replacement, and for each integer I drop a ball into the corresponding bucket. k can be ...
1
vote
1answer
160 views
Integral of a conditional uniform distribution leads to improper integral
I have two uniforms distributions, $X_1 \sim\it{U}(a,b)$ and $X_2\sim\it{U}(X_1+\delta,b+\delta)$. I would like to compute $P(X_2\in[a+\delta,b+\delta])$. So I do this:
$$\begin{eqnarray*}
...
6
votes
3answers
795 views
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 ...
0
votes
0answers
12 views
Test for two - dimensional uniform distribution? [duplicate]
Possible Duplicate:
Measure the uniformity of distribution of points in a 2D square
I have spatial data -coordinates on rectangle, how to test if they come from two dimensional random ...
1
vote
0answers
22 views
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 ...
19
votes
5answers
764 views
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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votes
1answer
121 views
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 ...
1
vote
1answer
80 views
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 ...
0
votes
1answer
33 views
Sampling subsegments from discrete input ranges
I have an set of input ranges {[a1, b1], [a2, b2], ...}. Each a and b represent integer ...
1
vote
1answer
105 views
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 ...
8
votes
3answers
372 views
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.
6
votes
1answer
126 views
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 ...
2
votes
2answers
366 views
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 ...
4
votes
3answers
200 views
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 ...
2
votes
1answer
146 views
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 ...
1
vote
0answers
231 views
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 ...
2
votes
1answer
328 views
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 ...
4
votes
2answers
1k views
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 ...
2
votes
1answer
101 views
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 ...
2
votes
1answer
230 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 ...
2
votes
1answer
552 views
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 ...
0
votes
1answer
152 views
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 ...
