The uniform distribution describes a random variable that is equally likely to take any value in its sample space.

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posterior distribution for coin flips given uniform prior distribution [closed]

A coin has an unknown head probability $p$. Flip $n$ times, and observe $X=k$ heads. Assuming an uniform prior for $p$, then the posterior distribution of $p$ is the beta distribution $B(\alpha = k + ...
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Transform {x_1t,…,x_nt }_(t=1)^T into uniform variables {u_1t,…,u_nt }_(t=1)^T in R? [closed]

i know that, how i could transform {x_1t,…,x_nt }_(t=1)^T into uniform variables {u_1t,…,u_nt }_(t=1)^T using the empirical distribution function?? and in R?
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15 views

Sum of uniformly distributed random variables over different intervals?

Let $\{X_i\}_{i=1}^N$ be $N$ random variables uniformly distributed over the intervals $[a_i, b_i]$ respectively. How does the sum: $$\sum_{i=1}^N X_i$$ distribute? This is a generalization of the ...
2
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1answer
27 views

Variance of uniform distribution

I can see how one can compute the variance of a uniform distribution on $[a,b]$ using $$ Var[X] = E[X^2] - E[X]^2 = \frac{(b-a)^2}{12}$$ as explained e.g. here: ...
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1answer
31 views

Bayes theorem with unknown model

I have a book on applied statistics that uses a result I don't understand. The example in the book begins with Bayes' theorem applied to hypothesis $H$ and data $D$: $$P(H|D) = \frac{P(D|H) ...
11
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4answers
345 views

Is there an explanation for why there are so many natural phenomena that follow normal distribution?

I think this is a fascinating topic and I do not fully understand it. What law of physics makes so that so many natural phenomena have normal distribution? It would seem more intuitive that they would ...
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3answers
82 views

Verifying that a random generator outputs a uniform distribution

I asked a student of mine this question: If you have a random number generator that outputs a number between $1$ and $k$, how would you write a test that decides whether the generated ...
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4answers
1k views

Is there a plateau-shaped distribution?

I am looking for a distribution where the probability density decreases quickly after some point away from the mean, or in my own words a "plateau-shaped distribution". Something in between the ...
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1answer
48 views

Discrete Distribution

In the die-coin experiment, a fair, standard die is rolled and then a fair coin is tossed the number of times showing on the die. Let N denote the die score and Y the number of heads. a)I want to ...
3
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1answer
84 views

Multi-variate uniform distribution

Suppose that $(X,Y,Z)$ is uniformly distributed on $\{ (x,y,z) : 0 \leq x \leq y \leq z \leq 1 \}$ a. I want to find out joint density function of $(X,Y,Z)$. b. I want to find out probability ...
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1answer
39 views

How to show $(n+1) \max(X_1, X_2, \ldots , X_n)/n$ is a method of moments estimator

If $X_i \sim$ uniform$(0,\theta)$, how can I show that the estimator $(n+1) \max(X_1, X_2, \ldots , X_n)/n$ is a method of moments estimator for $\theta$? For example, we know the first sample moment ...
2
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149 views

How to find a conditional CDF of a trapezoidal distribution?

I'm working on a game theory model of imperfect information, where players observe certain attributes via noisy signals. Specifically, Player 1 has the opportunity to choose any value $\eta$ from the ...
0
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1answer
35 views

Expected value of Uniform distribution

Suppose $X$ is an uniform random variable: $X \sim U(a,b)$. I know how to compute $E(X)$, but what if I want to compute: $E(X^\gamma)$ where $\gamma > 0$?
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1answer
43 views

Consider a random sample of size n from a uniform distribution, $X_i - UNIF(0,θ), θ>0$ and $X_{n:n}$ is the largest order statistic

Consider a random sample of size n from a uniform distribution, $X_i - UNIF(0,θ), θ>0$ and $X_{n:n}$ is the largest order statistic. What is the probability that $(X_{n:n}, 2X_{n:n})$ contains ...
3
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1answer
53 views

Interval of a transformation of a uniform variable

Suppose we have a uniform random variable $U$ which is defined on the $[0,1]$ interval. Consider the transformation:$$X=k\times \log(U)$$ How would I go about calculating the interval on which ...
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1answer
27 views

Question on confidence intervals for uniform distribution

I have a random variable $X$ which is distributed uniformly over $[0,b]$. I want to know based on only one observation what is the confidence level of the interval $[X, 4X]$? I know this entails ...
3
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2answers
62 views

How to find the CDF of a random variable uniformly distributed around another random variable?

I'm working on some game theory models of incomplete information (which I've posted about a few times here). I think this question is pretty straightforward though, so the actual context is ...
3
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1answer
92 views

How to compute the CDF of this random variable?

I'm working on a game theory model of incomplete information, where players observe certain attributes via noisy signals. Specifically, one player has the opportunity to choose any value $\eta$ from ...
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1answer
35 views

What is the density of the $m$'th element of a sorted vector of $n$ uniformly distributed random variables

$X_1, X_2, ..., X_n$ are independent and uniformly distributed on $[0, 1]$. Sorting them yields a vector, whose first and last element have densities that are just the derivatives of products of CDFs. ...
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3answers
209 views

Why does the number of continuous uniform variables on (0,1) needed for their sum to exceed one have mean $e$?

Let us sum a stream of random variables, $X_i \overset{iid}\sim \mathcal{U}(0,1)$; let $Y$ be the number of terms we need for the total to exceed one, i.e. $Y$ is the smallest number such that $$X_1 ...
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1answer
52 views

Probability the next draw from a distribution is greater than some number given a previous draw

I'm working on a game theory model of incomplete information, where players observe certain attributes via noisy signals. I am looking to solve for two different probability functions, though I think ...
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0answers
13 views

Distribution of samples from a uniform distribution [duplicate]

Let's say we are taking $n$ samples from a uniform distribution, that spans from $0$ to $1$. According to the central limit theorem, the mean of the $n$ samples will follow a normal distribution with ...
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79 views

Error in proof of $Y=F(X)$ uniform on $[0,1]$

If we let $Y=F_X(X)$ then $Y\sim U(0,1)$, which is proved in introductory texts in statistics (for example Casella and Berger Statisical Inference p. 54). What is then the error in the "proof" ...
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25 views

MLE Uniform X∈(N,N+1,…,N+10) [duplicate]

I am trying to find N by MLE for several discrete uniform distributions involving a parmeter N∈Z. If the interval X is defined on is X∈(N,N+1,...,N+10) then I think N^=min{X1,X2,...Xn}.But this ...
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1answer
54 views

MLE for discrete uniform distribution [closed]

I am trying to find $N$ by MLE for several discrete uniform distributions involving a parmeter $N\in \mathbb{Z}$. If the interval $X$ is defined on is $X\in (N,N+1,...,N+10)$ then I think ...
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Compound Distribution — Uniform Distribution with Normally Distributed Parameters

Could someone please point me to a source or suggest ways in which we can obtain the Distribution, Density Functions, Expected Value, etc. of a Uniform Distribution whose parameters are distributed ...
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252 views

Distribution of continuous uniform RV with upper limit being another continuous uniform RV

If $X \sim U(a, b)$ and $Y \sim U(a, X)$, then can I say that $Y \sim U(a, b)?$ I am talking about continuous uniform distributions with limits $[a, b]$. A proof (or disproof!) will be appreciated.
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1answer
39 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 ...
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1answer
52 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 ...
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1answer
86 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
25 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 ...
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48 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 ...
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How to plot prior distributions in R, particularly variance components?

I’m pretty new to R and struggling to replicate this prior distribution on the log(variance) scale: log⁡(τ^2)~Uniform(-10,1.386) From the paper I’m trying to replicate it from it should look like ...
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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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150 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 ...
3
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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 ...
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1answer
142 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
46 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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85 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
74 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 ...
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2answers
60 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 ...
10
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1answer
422 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
43 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 ...
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1answer
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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) = ...
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1answer
50 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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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
59 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 $u_1$, ...
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1answer
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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 ...
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1answer
59 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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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 ...