Researchers collaborate on scientific projects that are often measured by both the quantity and the quality of the resultant peer-reviewed 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.