Tagged Questions

47 views

Non-uniform sampling of N-sphere

Suppose I have a unit $N$-sphere from which I want to draw points at random. To obtain uniformly distributed points I do the usual technique of drawing $N$ random variables $x_i$ from a Gaussian ...
76 views

Convolution of two Uniformly distributed r.v. ove

Assume a continuous random variable $X$ that is uniformly distributed $\underline{\text{on}}$ a $k$-sphere. For simplicity, lets assume a simple circle with radius $R$ in 2 dimension. Therefore ...
72 views

How to characterize rotations in $\mathbb{R}^n$?

I am studying the performance of an optimizer algorithm to find the $$\textrm{argmin}_{x\in \mathbb{R}^n} f(x) \text{ where } f : \mathbb{R}^n \rightarrow \mathbb{R}$$ I would like to test how the ...
21 views

How to properly clamp Beckmann Distribution

I am trying to implement the Cook-Torrance Microfacet BRDF shading model and I am having some trouble with the Beckmann Distribution: Beckmann Distribution with width parameter ...
24 views

probability calculation for position measurement being inside a circle

Consider a position measurement that is prone to a random error in any direction. This would mean that the position would be in a circle where the probability curve taken across the diameter would ...
153 views

Determine if a set of points on a sphere come from a uniform distribution?

I have a large distribution of points on the unit sphere $S^2$ and I want to determine if those points came from a uniform distribution on the surface. Essentially, I'm looking for a two dimensional ...
91 views

What should be the proportions of a three sided coin?

A classical coin has almost no chances of ending its course on the side when tossed. A round pencil with both ends flat has no chance of ending its course on the tip, when tossed. What would be the ...