# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### Why isn't information theory taught in traditional classes on probability theory? [closed]

Information theory consists of several tools that can measure the information content of entire probability distributions, each one calculated purely from probabilities unlike traditional frequentist ...
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### Bounded probability distribution wanted [closed]

I am searching for a bounded continuous probability density function with the following two properties: (1) it should be a distribution of probabilities (i.e. it occupies the space [0; 1]) (2) as the ...
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### Bayes' Theorem Application

Ontario Public Health conducted a study on their test results for detecting SARS-CoV-2 (the virus that causes COVID-19) from Jan-April 20201. These are all patients who had symptoms and went to get ...
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### How to check for linearity assumption in GLM?

Let g be the link function, y be the target variable, and $\beta_1x_1$+... $\beta_nx_n$ for some $n \in \mathbb{N}$ be the linear predictor. One of the assumptions for a GLM states that there exists a ...
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### Can someone explain to me the sampling distribution of sample variance in comparison to that of the sample mean?

I have read tons of things already about the sampling distribution of the sample variance but I can't get quite a good grasp of exactly what it is like in terms of the formulas of the measurements. ...
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### Why can you not find the probability of a specific value for the normal distribution? [duplicate]

I am learning about the normal distribution and was watching this video. At 6:28, the question imposed is what is the probability of an ice-cream weighing exactly 120 grams (using the normal ...
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### Saddle point method used to calculate the inverse Fourier transform

Here I want to find the asymptotic behavior of the following integral $$f(x,t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\exp(-ikx)*\exp(t(1-\exp(-|k|^\beta)))dk,~~~~~~~Eq~1$$ where $x$ goes to infinity. ...
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### What test for verifying statistical significance for difference in 2 groups [closed]

How to verify the difference in estimated effects of 2 variables on a dependent variable using a statistical test. Q: Determine the estimated effect of X1 on retention, controlling for a,b,c, Include ...
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### Is Pr(A | B, C) = Pr (A | B) * Pr(B | C)? If not, what assumptions do I need to establish it?

I came across the following statement in a paper: $$Pr(A | B, C) = Pr (A | B) * Pr(B | C)$$ A, B, C are discrete variable. Right before this, they say that this comes from the assumption that the ...
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### Generating random numbers that are log-normally distributed

Even though I don't quite understand why and how this works, I appreciate how simple it is to generate a set of numbers which are Poisson distributed: ...
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### Error for operations for Two Poisson distributions

Can error (std dev) in A +B or A-B be $\sqrt{A}$+$\sqrt{B}$ if A and B are Poissonian? If yes, what would be similar expressions for AB and A/B ?
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### In these domains do they have different conditional probability distribution AND marginal probability distribution?

For simplicity, I'm going to focus on subject 1 and subject 4 and only observe class 3 (green) and class 2 (blue), here's my understanding: The have different conditional probability distribution, ...
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### Estimate rolling distribution of sign-up durations from time series?

Conceptual question: Suppose I have a times series (500 entries or so) of daily number of individuals signed up on a list, from the start of this list (i.e. zero people on it in the beginning). At any ...
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### Laplace-Stieltjes Transforms and distribution

I was going through a paper, I came across below relation, \begin{equation} T=\begin{cases} C, & \text{with probability $P(H<C)$}\\ 0, & \text{with probability $P(H>C)$} \...
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### When is mutual information difficult or easy to estimate compared to correlation?

I came across the following statement about covariance/correlation vs mutual information, Covariance can be calculated directly from a data sample without the need to actually know the probability ...
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### Does every statistic have a sampling distribution, not just the sample mean?

I am curious because most basic undergraduate statistics reference just start out Inferential Statistics by mentioning sampling distributions and the sampling distribution of the mean. My question is ...
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### Scaled sample variance as sum of squares of normal variables

I want to prove that $(n-1)S^2 = \sum_{i=1}^{n} (X_i - \bar{X})^2$ can be written as $\sum_{i=2}^{n} Y_i^2$, with $Y_i = N(0,\sigma^2)$, $X_i$ and $Y_i$ $i.i.d$. I managed to do it by taking a big ...
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### Does entropy have less estimation error than mean and variance estimates?

Estimating the mean or expected value of a continuous random variable's (r.v.) empirical distribution is known to be difficult, moreso than estimating the variance. Estimates of the mean and variance ...
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### What length are some segments of a broken rod?

If a rod (of unit length) is broken into $n$ segments (assuming the $n-1$ breaks occur with uniform probability across the entire length) and $k$ of those segments are chosen at random and laid end to ...
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### Estimate Unique Number of Visitors

Is there a way to estimate the number of unique monthly visitors to a site based on a limited sample of one week of data? I have information about when a given user visited the site. This isn't as ...
As far as I understand one can in principle model the distribution over a set of $k$ categories using e.g.: the Dirichlet distribution A softmax model. As far as I can tell, both use $k$ parameters ...
Suppose we have two different probability distributions $p, q$ defined on input $x \in [0,1]$. We know that for any value of $x$ in the domain, we have $\exp^{-a} \leq \frac{p(x)}{q(x)} \leq \exp^{a}$...