All Questions
10 questions
0
votes
0
answers
41
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Uniform density over 2 segments [duplicate]
Background
Let $V_1, V_2 \in \mathbb{R}^2$ be the vertices of a segment and let $z$ be uniformly distributed over that segment. Now consider the random vector
\begin{equation*}
\begin{aligned}
y&=...
- 473
2
votes
1
answer
382
views
What's the expression for convolution of a uniform[a,b] density and a normal(0,d^2) density?
Suppose I have $X\sim Uniform[a,b]$ and $Y\sim normal(0,d^2)$, what's the expression for the density of $Z=X+Y$?
Let $F_{Z}(z)$ be the cdf of $Z$ evaluated at $z$, and let $\Phi(\cdot)$ and $\phi$ be ...
- 3,050
3
votes
1
answer
1k
views
Sum of exponential of uniform random variables?
Let $F_{i}$ and $\phi_{i}$ are uniformly distributed independent random variables in the range $[-50,50]$ and $[-\pi/4,\pi/4]$, respectively.
If $N = 10$ and
$$Z = \sum_{i=0}^N e^{j(F_{i}+\phi_{i})}...
- 121
3
votes
1
answer
9k
views
Sufficient statistics in the uniform distribution case
I am currently studying sufficiency statistics. My notes say the following:
A statistic $T(\mathbf{Y})$ is sufficient for $\theta$ if, and only if, for all $\theta \in \Theta$,
$$L(\theta; \mathbf{y})...
- 2,204
2
votes
2
answers
411
views
What is the ratio of a N[0,1] and U[-1/2,1/2]?
I have come across a problem where I can reasonably assume that the numerator is a uniform distribution of the type U[-a,a], i.e., centered on zero, and the denominator is N[0,b]. This seems to be ...
- 13.3k
2
votes
1
answer
155
views
Transforming a uniform PDF to a Gaussian PDF
I have a Uniform PDF from [-50, 50], I would like to transform it to a Gaussian. The methods that I read up about doing this(like Box Mueller) assume that the uniform distribution is between [0,1). Is ...
8
votes
2
answers
1k
views
How is the spherical elevation angle distributed when $(x,y,z)$ are uniformly and normally chosen?
As a follow up to
How the polar coordinate, $\theta$, is distributed when $(x,y) \sim U(-1,1) \times U(-1,1)$ and if $(x,y) \sim N(0,1)\times N(0,1)$?
Assume $(x,y,z) \sim U(-10,10) \times U(-10,10) \...
- 739
21
votes
3
answers
8k
views
How is $\theta$, the polar coordinate, distributed when $(x,y) \sim U(-1,1) \times U(-1,1)$ vs. when $(x,y) \sim N(0,1)\times N(0,1)$?
Let the Cartesian $x,y$ coordinates of a random point be selected s.t. $(x,y) \sim U(-10,10) \times U(-10,10)$.
Thus, the radius, $\rho = \sqrt{x^2 + y^2}$, isn't uniformly distributed as implied by $...
- 739
3
votes
0
answers
122
views
Is the Gaussian distribution the only statistical distribution fully determined by the mean and variance?
I've read that the Gaussian marginal is fully determined by the mean and variance. What does this mean in reality? If we consider a Gaussian marginal PDF is given by
$$ \pi_G(\xi|\mu,\sigma) = {1\...
- 724
3
votes
1
answer
413
views
Scale parameter MLE scheme known but how to find according distribution PDF?
For known location, we can find the scale parameter of a normal distribution by calculating the sum of squared differences to the location, then dividing by n-1 and taking the square root. This is the ...
- 445