# Testing correlation coefficients from two bivarate poisson

I have datasets from two bivariate poisson distributions, $$BVP_x(\lambda_1, \lambda_2, \lambda_{12})$$, and $$BVP_y(\lambda_3, \lambda_4, \lambda_{34})$$ respectively.

Now we know the correlation coefficient for these two distributions can be defined as $$\rho_x = \frac{\lambda_{12}}{\sqrt{(\lambda_1 + \lambda_{12})(\lambda_2 + \lambda_{12})}}$$ and$$\rho_y = \frac{\lambda_{34}}{\sqrt{(\lambda_3 + \lambda_{34})(\lambda_4 + \lambda_{34})}}$$,

Is there a standard test for testing $$H_0 : \rho_x = \rho_y$$ vs $$H_1 : \rho_x \neq \rho_y$$, I understand this doable by likelihood ratio tests, but not sure if there is already existing distribution for testing the parameters.

I know for bivariate normal distribution Fisher's transformation and $$z$$ test would work. Would that also work for bivariate poisson.

• I would have to investigate this a bit further, but I believe the assumption of normality is for when you are looking at single sample estimates. If you are comparing two correlations, I am not sure this assumption is required, as the standard error of the transform for each will be approximately $\frac{1}{\sqrt{N_i-3}}$. May 29 at 15:11