This paper proposes a hierarchical Bayesian model for estimating the parameters of asymmetric power distributions (APDs). These distributions are defined by shape, scale and asymmetry parameters which make them very flexible for approximating empirical distributions. A hybrid Markov chain Monte Carlo method is then studied to sample the unknown parameters of APDs. The generated samples can be used to compute the Bayesian estimators of the unknown APD parameters. Numerical experiments show the good performance of the proposed estimation method. An application to an image segmentation problem is finally investigated.