Expressions for Rényi and Shannon entropies for bivariate distributions

Exact forms of Rényi and Shannon entropies are determined for 27 continuous bivariate distributions, including the Kotz type distribution, truncated normal distribution, distributions with normal and centered normal conditionals, natural exponential distribution, Freund's exponential distribution, Marshall and Olkin's exponential distribution, exponential mixture distribution, Arnold and Strauss's exponential distribution, McKay's gamma distribution, distribution with gamma conditionals, gamma exponential distribution, Dirichlet distribution, inverted beta distribution, distribution with beta conditionals, beta stacy distribution, Cuadras and Augé's distribution, Farlie Gumbel Morgenstern distribution, logistic distribution, Pearson type VII distribution, Pearson type II distribution, distribution with Cauchy conditionals, bilateral Pareto distribution, Muliere and Scarsini's Pareto distribution, distribution with Pareto conditionals and the distribution with Gumbel conditionals. We believe that the results presented here will serve as an important reference for scientists and engineers in many areas.