# Questions tagged [probability]

A probability provides a quantitative description of the likely occurrence of a particular event.

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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 $\sum_{1 \leq i \leq n}|x_i|$. $Y=|X|$ ...
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### Conditional probability update for correlated Poisson variables

Some background: I am trying to estimate the number of failures in two related machine populations. I model machine failures in a year as a correlated Poisson process as such: $Y_0,\ Y_1$ and $Y_2$ ...
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### What is p(data) in image generation

In the context of image generation architectures such as VAEs or GANs (say we are using mnist digits) what do we mean by probability distribution of the data? Just to clarify this question and make it ...
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### What conditions are needed for $a_n = O_p(n^d) \implies E[a_n] = O(n^d)$?

Let $X_n$ be a uniformly integrable sequence of random variables. In a recent question I asked about the possibility of converting Big $O_p$ convergence in probability of the sequence $X_n$ to Big $O$ ...
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### Summing predicted probabilities from logistic regression using 'one vs. rest'

I have a multiclass classification problem that I have solved using a 'one vs. rest' approach via binary logistic regression classifiers from Python's scikit-learn package. In my problem, there are 3 ...
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### Kolmogorov distributuon derivation

I would like to know if there is a book talking about the derivation of Kolmogorov distribution (Using usual definition for the bridge process) \begin{align} P(K\leq x)=1-2\sum_{i=1}^{\infty}(-1)^{i-1}...
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### Covariance of order statistics convergence?

Suppose I have a sample $(X_1 \dots X_n)$ and $(Y_1 \dots Y_n)$, all of which are $N(0,1)$ random variables. I am interested in the asymptotic behaviour of $$\frac{1}{n} \sum_{i=0}^n X_{(i)}Y_{(i)}$$...
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### Empirical multivariate probability integral transform

Is there a 'simple' way to obtain a non-parametric empirical multivariate probability integral transform? Univariate case The probability integral transform relates to the transform of any random ...
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