Adaptive Random Testing (ART) was developed to enhance the failure detection capability of Random Testing. The basic principle of ART is to enforce random test cases evenly spread inside the input domain. Various distribution metrics have been used to measure different aspects of the evenness of test case distribution. As expected, it has been observed that the failure detection capability of an ART algorithm is related to how evenly test cases are distributed. Motivated by such an observation, we propose a new family of ART algorithms, namely distribution metric driven ART, in which, distribution metrics are key drivers for evenly spreading test cases inside ART. Our study uncovers several interesting results and shows that the new algorithms can spread test cases more evenly, and also have better failure detection capabilities.