2
votes
1answer
302 views

Do the properties of Pearson's chi-squared test for independence hold true for continuous PDFs?

In probabilist statistics, the properties of a discrete Pearson's chi-squared test hold that: \begin{aligned} \chi^2 = \sum_{i=1}^{r} \sum_{j=1}^{c} {(O_{i,j} - E_{i,j})^2 \over E_{i,j}} ...
2
votes
0answers
64 views

Density related to sparseness measure

Are there any multi-variate continuous distributions whose probability distribution functions give high values for sparse vectors and low values for dense vectors, i. e. indicating the sparseness of ...
5
votes
2answers
511 views

What is the best way to discretize a 1D continuous random variable?

Say I have a 1-dimensional continuous random variable $X$, with PDF $f(X)$, CDF $F(X)$ and inverse CDF $F^{-1}$. What is the best way to discretize $X$? To keep things clear, let $Y$ denote the ...