When analyzing biomedical data, researchers often need to apply the same statistical test or procedure to many variables resulting in a multiple comparisons setup. A portion of the tests are statistically significant, their unadjusted p-values form a spike near the origin and as such, they can be modelled by a suitable Beta distribution. The unadjusted p-values of the non-significant tests are drawn from a uniform distribution in the unit interval. Therefore the set of all unadjusted p-values can be represented by a beta-uniform mixture model. Finding the parameters of that model plays an important role in estimating the statistical power of the subsequent Benjamini-Hochberg correction for multiple comparisons. To empirically investigate the properties of some parameter estimation procedures we carried out a series of computationally intensive numerical simulations on a high-performance computing facility. As a result of these simulations, in this article, we have identified the overall optimal method for estimating the mixture parameters. We also show an asymptotic property of one of the parameter estimates.