All Questions
Tagged with convolution probability
286
questions
1
vote
0
answers
50
views
Finding the general convolution of probability function with hypergeometric PDFs.
I am trying to find the generalized convolution of this PDF distribution.
$$f(n, \sigma; v)= \frac{2^{\frac{3}{2}-\frac{n}{2}} \sigma ^{-n-1} v^\frac{n - 1}{2} K_{\frac{ n - 1}{2}}\left(\frac{v}{\...
- 21
0
votes
0
answers
22
views
Help with understanding combination of probability distributions
I have two probability mass functions (PMFs) across the surface of a sphere. They are localised Gaussians (a few degrees in expanse), whose centres have arbitrary positions though they are quite close ...
0
votes
2
answers
66
views
Differentiating Entropy with respect to Convolution Parameters
First, some formula reminders for the sake of completion:
$H(X) = -\sum_{i} p(x_i) \log p(x_i)$ is the entropy of a sequence $x_i$, where $p(x)$ is the discrete probability of x.
A discrete ...
- 65
0
votes
0
answers
35
views
Dependent random variables whose convolution adds up
I want to find two dependent random variables $X$ and $Y$ with values in $\mathbb{Z}$ such that $P_X\star P_Y=P_{X+Y}$, where $\star$ is the convolution.
What I've tried:
I was "tickling" ...
- 1,279
0
votes
0
answers
36
views
Preservation of strict log-concavity under convolution
I have spent an embarrassing amount of time trying to prove or disprove any of this. I am aware that a similar question was posted in 2014, but since I couldn't make anything out of the two sources ...
- 13
2
votes
1
answer
67
views
Probability that a uniform random variable + a constant be greater than another uniform random variable
I am trying to understand a model of probabilistic voting from the following paper https://ideas.repec.org/a/eee/pubeco/v96y2012i1p10-19.html and the one component I struggle with goes as follows:
ΔU ...
- 23
0
votes
0
answers
43
views
Solution to convolution integral equation
I have two positive definite kernels $k_1,k_2 : \mathbb R^d \to \mathbb R$ and a probability measure $\rho$ on $\mathbb R^d$. The kernels are of the form $k_i(x,y)=K_i(x-y)$ for some function $K_i:\...
- 182
0
votes
0
answers
61
views
Probability density function of three independent random variables
I will try to describe the question first and how i solve the problem.
Here we have three independent random variable $X,Y,Z$ and $S_3=X+Y+Z$,
the probability density function of three variable are ...
- 1
1
vote
1
answer
68
views
"Deconvoluting" the sum of independent random variables
I encountered the following question in my research. See here for some background, but this post should be self-contained. Suppose
$X$ follows a discrete uniform distribution on $m$ points $\{X_1, ...
- 836
1
vote
1
answer
71
views
How does this density function make sense?
Let $X$ be an exponentially distributed random variable with parameter $\beta>0$ and let $Y$ be a random variable with $P(Y=0)=1-p$ and $P(Y=1)=p$, where $0<p<1$. Assume that $X$ and $Y$ are ...
- 59
1
vote
1
answer
78
views
Convolution of random variables - confusion about change of variables
Consider
I understand everything except of the first line of the note. In particular
$$
\int_\Omega 1_{X(\omega ) + Y (\omega )\in A} \;d \mathbb P(\omega ) =\iint \mathbf{1}_A (x+y) \; \;d(\mu, \nu)...
- 2,302
0
votes
0
answers
71
views
Seeking Probability Function Invariant under Normal Gaussian Convolution
I'm currently working on a problem where I need to find a probability function,
$P(x)$, that remains unchanged after a normal Gaussian convolution. Specifically, the function should satisfy the ...
- 770
0
votes
0
answers
31
views
Is the modulo-2 addtion of two random variables a convolution?
Let's say we have two random discrete variables. Given an arbitrary element $y$ in $[0, 2^{n}-1]$, we compute the probability of $y$, where $y = x + b \mod 2^{n}$ by:
$$P(y) = \sum_{x=0}^{2^{n}-1} (P(...
- 159
1
vote
1
answer
107
views
Show the renewal function is differentiable
Definition.
For a sequence of $\text{i.i.d.}$ random variables $ \left\{X_{k},k\ge 1 \right \},$called
inter-renewal times, let $S_{n}=\sum_{k=1}^{n}X_{k},n\ge 0,$ be the time instant of the $n$th ...
- 204
0
votes
1
answer
147
views
Convolution of pdfs of $\textrm{Uniform}[0,1]$ and $\textrm{Uniform}[1,2]$
Let X a random variable following the uniform distribution over $[0,1]$
Let Y a random variable following the uniform distribution over $[1,2]$
be independent random variables, whats is the ...
- 225