Unanswered Questions
2,852 questions with no upvoted or accepted answers
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Are these equivalent (for p-values): super-uniform, stochastically larger than / dominating the uniform, conservative?
In the literature and online, I have found three different wordings that I think refer to the same concept: stochastically larger than uniform (which I take is ...
CommunityBot
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8
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Concentration of maximum of subexponential random variables
I'm looking for a concentration bound on the maximum of a collection of sub-exponential random variables, which are not necessarily independent. More specifically, I have the following collection:
\...
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Sum of absolute values of T random variables
Where X is a r.v. following a symmetric T distribution with 0 mean and tail parameter $\alpha$.
I am looking for the distribution of the n-summed variable $ \sum_{1 \leq i \leq n}|x_i|$.
$Y=|X|$ ...
- 84k
8
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Finding the distribution of sample range for a Beta population
Let $X_1,X_2,\ldots,X_n$ be i.i.d random variables having density
$$f(x)=2(1-x)\mathbf1_{0<x<1}$$
I am trying to derive the distribution of the sample range $R=X_{(n)}-X_{(1)}$.
The usual way I ...
CommunityBot
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7
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How to explain the difference between confidence and credible interval?
The key difference between Bayesian statistical inference and frequentist statistical methods concerns the nature of the unknown parameters that you are trying to estimate. In the frequentist ...
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7
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What is the difference between a "population," a "sample space," an "underlying probability distribution? and a "model"?
I'm trying to understand an overview of the topic of statistical inference. I have learnt bits and pieces of many of the probability and statistics involved in it but before learning it rigorously it ...
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Strange connection between Bernouilli, Uniform and Geometric distributions
Final update on 11/29/2019: I have worked on this a bit more, and wrote an article summarizing all the main findings. You can read it here.
Let us consider $Z = X_1 + X_1 X_2 + X_1 X_2 X_3 +\cdots$ ...
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Distribution of the $L^2$ norm of a vector of components drawn from uniform distributions
We consider a random vector $\vec{v} = \left(x_{1}, x_{2}, \dots, x_{n}\right)$ built from $n$ real random variables drawn from a real continuous uniform distribution $\mathcal{U\left(a, b\right)}$, $...
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How were statistical distributions discovered?
Let me start, that i know that it's not very difficult to generate a probability distribution. If one takes any positive integrable function and normalizes it, this results in a probability density. ...
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Square roots of sums absolute values of i.i.d. random variables with zero mean
In an earlier question, I asked about the limiting distribution of the square root of the absolute value of the sum of $n$ i.i.d. random variables each with finite non-zero mean $\mu$ and variance $\...
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What bounds can we place on approximation error for a moment-matching approximation with $N$ moments?
Suppose I have a distribution over the real line ($p$) and I'm approximating it by matching its first $N$ moments. What can I say about the approximation error as a function of $N$?
Alternatively, ...
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Goodness-of-fit for Discrete Distributions
I've been doing some data analysis with Scipy. So far I accomplished this with continuous distributions:
I can fit a probability distribution to a set of data points using a maximum likelihood fit. ...
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How to compare models with different distributional assumptions for response variable in GLM?
Let's say I have measurements $Y$ which are all positive, and the distribution seems to be somewhat skewed. I'm modelling $Y$ in GLM framework. Now I could set my GLM using different distributional ...
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Test for difference of distributions on a torus
I have two circular dependent variables and would like to test for a difference in the distributions (presumably circular means) between multiple treatment groups. There are a number of multivariate ...
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7
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Exchangeable Processes over the Simplex
You are likely all familiar with Polya Urn process. I initially start with an urn containing $b$ black balls and $w$ white balls. At each step, I sample a black ball with probability $\frac{b}{b+w}$ ...
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