Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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Why Pearson correlation coefficient follows beta distribution? [duplicate]

I understand that the pearson correlation coefficient r can be tested using student-t distribution. Also I can understand the exact distribution of r from https://en.wikipedia.org/wiki/...
266 views

Fitting measured, real-world data to theoretical distribution: How to test goodness?

I have a large sets of real-world user data (30k, 80k, 90k measurements). To be precise those are simply session lengths for a specific system. I want to create a theoretical model of this, to ...
250 views

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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Maximum Likelihood vs. Restricted Maximum Likelihood vs. Penalized Maximum Likelihood

I am trying to better understand the differences between the Maximum Likelihood vs. Restricted Maximum Likelihood vs. Penalized Maximum Likelihood. In general, here is what I understand so far: The ...
3k views

What is "the shortest half of the data"?

Here is a histogram (realized with JMP) displaying two types of box plot called outlier box plot and quantile box plot. Right below, there are a bunch of explanations of the meaning of the different ...
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When you do a random permutation F test (by permuting group membership) is inference made on the samples or the populations?

I am trying to understand different approaches that use randomization procedures. One thing I cannot come to a clear conclusion on is this: Say we have randomly sampled individuals from 2 populations. ...
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Extreme values and skewness in data for machine learning

I have 2 classes that I want to train a model with. Looking at histograms of the features shows that most of the features have some very large outliers, and some of the distributions are skewed. My ...
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What is the appropriate distribution of Ordinal Data?

I have an ordinal random variable {0,1,2,3}. The variable should describe disease severity. What kind of probability distribution is the best fit to model this variable? The categorical distribution ...
319 views

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How are copulas used in the real world?

I have been reading about copula models. Essentially, copula models seem to be a creative method for creating a joint probability distribution from several variables, in which each individual variable ...
1k views

covariance matrix of residuals from a fitted model to decorrelate residuals

I fit a geeglm model with clustered data and now I would like to decorrelate the residuals of the model in order to run model diagnostics. I read that if I can obtain the covariance matrix of the ...
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Cramér–von Mises criterion vs Goodness of Fit

I had the following question about the Cramér–von Mises (CVM) criterion vs Goodness of Fit As described above, it seems like the CVM test measures how close the empirical probability distribution ...