# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### ANOVA (assuming different distributions) vs Kruskall-Wallis and post-hoc tests

During stats courses on Uni I learnt (if I remember correctly and hopefully don't put my teachers to shame) that if you want to compare multiple groups with eachother you look at the residuals of an ...
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### What is the correct procedure for adding random noise to observed predictor data in order to generate binary response data?

Suppose we have an observed data matrix $X$ of length $N$ with $2$ column predictors. If I wanted to generate continuous response data from this, we might do $$Y^{cont} = X\beta + N(0,1)$$ or in <...
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### What is the assumption on the distribution of data in gaussian mixture models?

I am reading about Gaussian mixture models from this slide https://www.ics.uci.edu/~smyth/courses/cs274/notes/EMnotes.pdf However, I am super confused at the very first line. It says: We ...
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### Impurity measurement of a group

I tried to use Gini Impurity to measure the impurity of a group of animals but is having trouble adding the distance between different animals to the equation. For example, the gini impurity of group (...
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### Exponential vs Gaussian Distribution in time problems

I'm wondering what about exponential distribution makes them better suited for time problems than gaussian distribution. For example, if I know that on average it takes the pizza delivery 20 minutes ...
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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. ...
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. ...
### Maximum likelihood estimator of $\theta$ for uniform distribution [closed]
For Uniformly Distributed random variables $X_1,X_2,\dots,X_n$ $\in \mathcal{R}$, the p.d.f is given by: $f(x_i) = 1/θ$ ; if $0≤x_i≤θ$ $f(x) = 0$ ; otherwise If the uniformly distributed random ...