Search Results

There are many ways to define bivariate beta distributions, that is, bivariate distributions on the square $[0,1]\times [0,1]$ with beta marginals.One way is to start with the usual stochastic representation … We could try with some more flexible bivariate beta distributions! …

The definition at How to Compute Bivariate Empirical Distribution? with $\le $, where you have $<$ is more usual, but I have seen your definition in some French books ... …

While that gives the derivation in the case of the difference $X-Y$ of two independent Poisson variates, not necessarily with the same mean, the OP seems to ask for the case of a bivariate Poisson distribution …

First, $\DeclareMathOperator{\P}{\mathbb{P}} \P(X Y > 0) = \P(X>0, Y>0 ~\text{or}~ X<0, Y<0)$ which is $2 \P(X>0,Y>0) ~~\text{(by symmetry)} $ Let us evaluate this by integrating a bivariate normal …

Partially answered in comments: The geometric analysis in my post can be used to show the expected proportion of exceptions when the data are bivariate Normal (which is what this calculator assumes) is …

Start with some bivariate copula see Introductory reading on Copulas, and then you can transform the marginals separately. (I will come back adding an example) …

First simulate $(U_1, U_2)$ from a bivariate copula you must choose. Then $U_1$ will be uniform on $(0,1)$ as will $U_2$, by the definition of a copula. …

Using the results from wikipedia page of Chebyshev's inequality (first inequality in section "two correlated variables"), I dont see anything for your case with one-sided inequalities. The more usua …

Hint: If $\sigma=1$, so you have two independent standard normal random variables, the the distribution of the radius squared is chi-squared with two degrees of freedom. For general $\sigma$ you have …