# Questions tagged [mathematical-statistics]

Mathematical theory of statistics, concerned with formal definitions and general results.

4,378 questions
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### A question about the definition of sample

Let $(\Omega,\Sigma,\mu)$ be a measure space. The definition of a sample is that it is a sequence of iid random variables $X_1,\ldots,X_n$. Usually random variables are real valued and the ...
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### How to test the validity of Fitt's law in R

I would like to use the Fitt's Law to test some hypothesis. Anyway, it's the first time I use it, and I have some doubts. Then aim of my experiment is to test if in a certain situation the Fitt's law ...
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### How do you verify independence of a pair of uniform random variables in MATLAB? [closed]

If $A$ is a subset of $R$ and $X$ is a random variable. I have two variables $X_1$ and $X_2$. $I$ being $1$ if $X$ in subset $A$, and $0$ if not in $A$. Let $U$~$U(0;1)$ and determine if this pair ...
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### How to write diff() mathematically?

I am using R/Python diff() operation. e.g., https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.diff.html I would like to know if there is a ...
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### Pointwise Mutual Information using spacy or just detailed explaination

So, I have been trying to play around with NLP recently and decided to work on a project involving Emotional Analysis. I have been following this particular research, http://www.cse.yorku.ca/~aan/...
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### How can we call likelihood function a joint PDF when the individual terms do not represent Probabilty

My understanding of the Probabilty Density Function is that they evaluate to 0 at a particular point . So if we have some i.i.d points $x_{n}$ from a Normal distribution and we write : ...
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### Encoding quantitative outputs for regression

From Elements of Statistical Learning: For a two-class G, one approach is to denote the binary coded target as Y , and then treat it as a quantitative output. The predictions Yˆ will typically ...
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### How to denote token length in statistics

I have a vocabulary (V) that includes terms. (e.g., V = ['data mining', 'data', 'machine', 'machine learning']) I also have a ...
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### If $X$ is from (canonical) exponential family, do we always know the distribution of $T(X)$?

Assume $X$ are generated by a distribution from exponential family, $$f(X; \theta) = h(X)\exp\{\eta(\theta)T(X) - b(\theta)\}$$ After solving several exercises with various distribution functions, ...
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### In k-means clustering, why sum of squared errors (SSE) always decrease per iteration?

In k-means clustering, why sum of squared errors (SSE) always decrease per iteration? How can prove it by mathematical derivation of formulas? k : number of clusters m : number of examples $c_h$ : ...
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