Based on a variant of the Simon model, it is shown that when the growth of the different word follows Heaps law with exponent being in (0,1), the power-law exponent is identical with the Heaps exponent.A biparameter power-law distribution,i.e., the Waring distribution, is derived within the framework of the Simons model.The estimator of the parameters of the Waring distribution is considered and numerical illustrations is provided.