Researchers collaborate on scientific projects that are often measured by both the quantity and the quality of the resultant peerreviewed publications. However, not all collaborators contribute to these publications equally, making metrics such as the total number of publications and the H-index insufficient measurements of individual scientific impact. To remedy this, we use an axiomatic approach to assign relative credits to the coauthors of a given paper, referred to as the A-index for its axiomatic foundation. In this paper, we use the A-index to compute the weighted sums of peer-reviewed publications and journal impact factors, denoted as the C-and P-indexes for collaboration and productivity, respectively. We perform an in-depth analysis of bibliometric data for 186 biomedical engineering faculty members and from extensive simulation. It is found that these axiomatically weighted indexes better capture a researcher's scientific caliber than do the total number of publications and the H-index, allowing for fairer and sharper evaluation of researchers with diverse collaborative behaviors.