All Questions
Tagged with convolution probability-distributions
228
questions
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50
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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
2
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1
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79
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Proving a distribution is not infinitely divisible
I'm trying to show the following:
Show that the distribution on $\mathbb R$ with density $f(x) = \frac{1-\cos(x)}{\pi x^2}$ is not infinitely divisible.
The characteristic function of this ...
- 4,075
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12
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Convolution of slightly multivariate Gaussians slightly modified
Starting with
$ p(a) = \int p(a|b) p(b) db$
replace $p(b)$ with $\tilde{p}(b) = \mathcal{N}(b; \mu_b, \Sigma_b + \tilde{D})$
where $\tilde{D}$ is an additive diagonal covariance.
Assuming ...
- 121
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35
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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
1
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38
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convolution-like computation of bivariate distribution
I would like to optimize code to compute a bivariate distribution like this (for example the bivariate poisson distribution):
$f_{n,m} = \sum_{i=0}^{n-1} a_i \times b_{n-i} \times c_{m-i}$
It really ...
- 11
1
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0
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27
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Approximating Linear Combination of Independent Random Variables
Let $X_i$ be independent, discrete random variables each with a known distribution and $\lambda_i$ be unknown real numbers. I am interested in running a linear optimisation over the $\lambda_i$ ...
1
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39
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Are there any interesting families of probability measures on $\mathbb{R}$ closed under convolution and "deconvolution"?
To define the property I am interested, let me introduce a notion of convolution measure on a measurable monoid $\mathcal{S}$. However, I am predominantly interested in the case where $\mathcal{S} \...
- 170k
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61
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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
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1
answer
79
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Sum of frequency distributions vs convolutions
From my understanding, the sum of independent random variables will be the same as the convolution of the input distributions.
However, when experimenting with it, I see the distribution of the sum of ...
- 143
1
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1
answer
68
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"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
0
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71
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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
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0
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51
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Convolution of two PDF
I am probably overlooking like, all the important details, but when trying to work out how to take the convolution of two pdfs I am going as follows:
according to https://en.wikipedia.org/wiki/...
- 1
1
vote
1
answer
145
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Sum of uniform and beta distribution
Suppose $X ∼ Beta(a = 3; b = 1; θ = 1)$ and $Y ∼ U (−2, 2)$ are independent. Derive an expression for the cumulative distribution function of $X + Y$.
I am trying to do this by a convolution but I am ...
- 13
0
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1
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147
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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
1
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1
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104
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Understanding convolution formula for density function
Let $X$ and $Y$ be uniformly distributed, independent random variables on $[0,1]$. Put $Z = X-Y$. How can I obtain the density function of Z?
I understand the following solution by geometric ...
- 75