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How to write a joint kernel density of two random variables with known individual densities?
Consider two random variables $X$ and $Y$ with densities
$${f}_1(x) = \frac{1}{n_1h_1} \sum\limits_{i=1}^{n_1}K\left(\frac{x-u_i}{h_1}\right) ~~~~\text{and} ~~~~ {f}_2(y) = \frac{1}{n_2h_2} \sum\...
- 765
0
votes
0
answers
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Computation of the density of the ratio of two random variables
Background:
For two continuous random variables, $X$ and $Y$, the density of $Z := \frac{X}{Y}$ is given by
\begin{equation}
p_Z(z) = \int_{-\infty}^\infty \lvert y\rvert\, p_{XY}(zy, y) \, \text{...
- 111