As we approach the era of exascale computing, the role of distributions to summarize, analyze and visualize large scale data is becoming more and more important. Since histograms continue to be a popular way of modeling the underlying data distribution, we propose a scalable and distributed framework for computing histograms from scalar and vector data at different levels of detail required by various types of analysis algorithms. We present efficient parallel techniques for histogram computation from regular as well as rectilinear grid data. We also study a technique called cross-validation to estimate the quality of computed histograms as a model of the actual data distribution. We parallelize cross-validation in a scalable manner to support histogram evaluation and selection of histogram parameters such as number of bins. We also present our distributed software framework for supporting science applications which require large scale distribution-based data analysis. The presented case studies highlight how the proposed algorithms and the related software benefit information theoretic and other distribution-driven analysis.