# Questions tagged [uniform-distribution]

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

761 questions
Filter by
Sorted by
Tagged with
25 views

### KL-Divergence on Uniform Distribution, is this correct?

$P_1$ is uniform on $[0, 0.5], ~P_2$ is uniform on $[0, 1]$ What is the KL-divergence $(P_1 \Vert P_2)?$ Attempt: $$D(p\Vert q) = \sum_{x\in X} p(x) \log \frac{p(x) }{q(x) }.$$ KL$(P_1\Vert P_2) =$...
• 215
1 vote
47 views

### Are there better measures of entropy

Related question here I am trying to measure the uniformity of multimodal distributions and am looking into using entropy. I would like a measure of entropy that is higher for the first distribution ...
108 views

### Why does somebody argue that the number of bootstrap replications should not be a multiple of 10?

At a recent conference somebody claimed that the size of the bootstrap replications should always be 999 rather than 1000. Which argument supports this claim?
• 289
1 vote
46 views

### How to Justify this Two-Sided Test is UMP with NP Lemma?

UMP tests generally do not exist for two sided tests, ie $H_0: \theta = \theta_0$ vs $H_a: \theta \neq \theta_0$. However, if we observe $n$ iid observations of $X\sim Unif(0,\theta)$, we can ...
• 89
48 views

### Joint Uniform Distribution Probability Problem

Let $X \sim U(0,1)$ and $Y \sim U(0,x)$. Calculate $$\Pr(X >0.5 | Y= 0.25)$$ Is this a trick question ? Since $\Pr(Y = 0.25) = 0$, right ?
221 views

### General form of the distribution of distances to a fixed point in rectangle

The answer given to the question Probability distribution of the distance of a point in a square to a fixed point solves for the "distribution of the distance between the origin (0,0) and a ...
• 3,348
15 views

### Convergence of a function having a big summation at each sample

I have the following function. $$x(k) = \sum_{m} e^{i (U_m k + \beta_m)}$$ Here, $U_m$ samples are random numbers coming from a Gaussian distribution $$U_m \sim \mathcal{N}(\mu_u, \sigma_u)$$ and ...
• 99
1 vote
48 views

• 327
86 views

### probability that the players will exchange their initially drawn number

Consider the following two-player game. The players simultaneously draw one sample each from a continuous random variable X, which follows $Uniform\ [0, 100]$. After observing the value of her own ...
46 views

• 61
35 views

• 161
680 views

### In Bayesian models, can you use Uniform(-inf, inf) as a prior?

In Bayesian models, can you use Uniform(-inf, inf) as a prior? I ask because in an class, we looked at MH MCMC sampler, and showed that to sample from a distribution, we need not explicitly solve for ...
• 1,728
1 vote
61 views

### What distribution is produced by the correlation of random values sampled uniformly?

I'm trying to figure out what this distribution is so that I can calculate the exact probability of values close to 1 or -1 using its PDF: as produced by the following code in R: ...
• 198
46 views

### ks test for uniform distribution

My question is similar to this post (KS test for Uniformity). KS p-valuse changes when samples are in different position, even if they have the same intervals. For example: ks.test(c(1,2,3),"...
• 1
### Find marginal distribution of Y while knowing distribution of X and $Y|X$
Assume that X is uniformly distributed on (0, 1) and that the conditional distribution of Y given $X = x$ is a binomial distribution with parameters $(n, x)$. Then we say that Y has a binomial ...