As the title says, I'm currently trying to find a distribution $p(\cdot)$ satisfying
- $p(x) = \int_0^\infty \exp(\lambda_1 y^2 + \lambda_2 x y) p(y) dy$
- $\forall x < 0 : p(x) = 0$
The only way I have so far thought of trying was to search for multivariate distributions with equal marginals where the conditional distribution $p(x \mid y)$ is of the form $\exp(\lambda_1 y^2 + \lambda_2 x y)$.
Any help on how I can tackle this problem is greatly appreciated!