Questions tagged [stable-distribution]
The stable-distribution tag has no summary.
36 questions
1
vote
0
answers
104
views
Reconstruct images with CLIP image embedding
I recently started working on a project that solely uses the semantic knowledge of image embedding that is encoded from a CLIP-based model (e.g., SigLIP) to reconstruct a semantically similar image.
...
- 11
4
votes
1
answer
112
views
Why does the stable distribution become Gaussian at $\alpha=2$?
I'm having trouble understanding why the stable distribution turns into a Gaussian at $\alpha=2$. In my course it seems like the idea is to see this from the tail behaviour of the distribution. From ...
- 43
1
vote
0
answers
76
views
Non-negative fat-tailed "almost stable" family of distribution with finite mean?
I am looking for a finite-dimensional family of distributions $F_X(x)$ with all the following properties:
Supported on $[0, +\infty)$,
Fat tailed, i.e. $(1-F_X(x)) \sim x^{-\alpha}$ for $x\to +\infty$...
- 247
3
votes
0
answers
165
views
Distribution closed under convolution and truncation followed by convolution
Let $D(\theta)$ denote an absolutely continuous distribution on $\mathbb{R}$. (The finite dimensional vector $\theta$ collects the parameters of the distribution.) Assume that the p.d.f. of $D(\theta)$...
- 565
0
votes
0
answers
64
views
Partial first moments of stable distributions?
Given a stable distribution with parameters $(\alpha, \beta), \alpha>1$ is it true that its all first partial moments (i.e. the integrals of the form $\int_a^b x f(x) dx$, where $a$ and $b$ could ...
1
vote
0
answers
89
views
Estimation of ARMA model with alpha-stable power GARCH errors
I am trying to write the following code for estimating parameters for the ARMA(1,1) with alpha-stable power-GARCH(1,1) (Mittnik et al. (2002)).
My code has 2 problems: 1) estimated parameters have a ...
- 11
2
votes
0
answers
132
views
Is sample mean an 'efficient' estimator for alpha stable distribution?
The question is just like the title. But...$\alpha$-stable distribution (for $\alpha\in (1,2)$) does not have the second moment, so the sample mean doesn't have variance well defined. Then for such a ...
Robert
-1
votes
1
answer
106
views
Show That $\sum_{K=1}^{n}\frac{X_k}{n^{\frac{1}{\alpha }}}$ If ${X_n}$ is $X_k$s Same Distribution
Let ${\{X_n}\}$ be a sequence of independent random variables and the
stable distribution of order alpha $(0\le\alpha\le2)$.
Show that $$\sum_{k=1}^{n}\frac{X_k}{n^{\frac{1}{\alpha }}}$$ if
${X_n}$ is ...
- 11
9
votes
1
answer
336
views
Do Lévy α-stable distributions maximize entropy subject to a simple constraint?
Is there a simple constraint on real-valued distributions such that the maximum entropy distribution is Lévy α-stable? Special cases include the Normal and Cauchy distributions for which the answer is ...
- 240
4
votes
0
answers
202
views
What is the limiting posterior in the generalized Bayesian central limit theorem?
The central limit theorem characterizes the limiting distribution of the sum of increasingly many finite-variance independent random variables: the limit is Gaussian. The generalized central limit ...
- 240
1
vote
0
answers
61
views
"Stable" distributions with integer support?
My understanding of stable distributions is that in order for a distribution to be stable, linear combinations of independent random variables from a given distribution (for example, a Gaussian) must ...
- 111
13
votes
1
answer
616
views
Random variables $X, Z$ such that $Z$ and $\sqrt{X + Z}$ have the same distribution?
I am looking for the distribution of a random variable $Z$ defined as
$$Z = \sqrt{X_1+\sqrt{X_2+\sqrt{X_3+\cdots}}} .$$
Here the $X_k$'s are i.i.d. and have same distribution as $X$.
1. Update
I ...
0
votes
0
answers
99
views
why are stable distribution called stable?
I know what a stable distribution is but I don’t know why do they call it Stable
I am not aware of anybody who is known by stable.
Is it possible because sum of a random variables end up with ...
- 373
4
votes
0
answers
122
views
Multivariate stable distribution
I know that if $\pmb{X}_1$ and $\pmb{X}_2$ are independent copies of a $n \times 1$ random vector $\pmb{X}$, then $\pmb{X}$ is said to be sum stable in $\mathbb{R}^n$ if $a\pmb{X}_1 + b\pmb{X}_2 \...
- 785
4
votes
0
answers
74
views
Difference between a translationary invariant and a stable distribution
I understand that a stable distribution is a distribution whose linear combination of two independent random variables with this distribution has the same distribution (ignoring location and scale ...
- 141