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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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 ...
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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 ...
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Where is the uniform distribution with one parameter ($U(\theta, k \theta)$) useful for modelling?

I recently came across the distribution $U(\theta, k \theta)$ (where k is known) in the context of statistical theory (as a nice toy example for finding MLE and the likes). However, I was wondering ...
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Proof help: Coincidences in higher dimensions

Background I recently watched a 2014 Talk by Geoffrey Hinton (a key researcher in Machine Learning literature) where he discusses the concepts behind the recently published Capsule Networks. In the ...
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It is true that $\mathbf X \sim F_X \Rightarrow F_X(\mathbf X) \sim U_{[0;1]}$; does the converse hold for multivariate $\mathbf X$?

For a univariate real-valued random variable I am pretty sure that the converse holds. Consider a multivariate $\mathbf X$ with values in $\mathbb R^n$ with measure $\mu(X)$ and its multivariate CDF ...
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Simplest possible (uniform) sampling of the interval [0,1] with n points

The simplest possible sampling of a function in the region [0,1] for the purpose of finding the area under the curve, for instance, could be just take the left offsets of the bars. That is, you have ...
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Inconsistent results with Monte Carlo solutions to similar problems in probability

I am presently going through the book Fifty Challenging Problems in Probability with Solutions and implementing Monte Carlo solutions to most of the problems in R to get familiar with the language, ...
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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 ...
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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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Finding MLE with ordered statistics?

Let Y1 < Y2 < ... < Yn be the order statistics of a random sample of size n from the uniform distribution of the continuous type over the closed interval: $$[\theta - \rho, \theta + \rho]$$ ...
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Transforming a uniform-on-sphere random vector

Consider the 3-D real random vector $(X_1,X_2,X_3)$ which is uniformly distributed on the surface of a unit sphere. What can be told about the distribution of $(aX_1,bX_2,cX_3)$, where $a,b,c,$ are ...
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Interarrival time distribution of uniform arrival process

I am currently trying to model an uniform arrival process within my simulation model. However, I can only model it by means of an interarrival time (I can let the model wait for a certain amount ...