The Phistogram

This article introduces a new kind of histogram-based representation for univariate random variables, named the <i>phistogram</i> because of its perceptual qualities. The technique relies on shifted groupings of data, creating a color-gradient zone that evidences the uncertainty from smoothing and highlights sampling issues. In this way, the phistogram offers a deep and visually appealing perspective on the finite sample peculiarities, being capable of depicting the underlying distribution as well, thus, becoming an useful complement to histograms and other statistical summaries. Although not limited to it, the present construction is derived from the equal-area histogram, a variant that differs conceptually from the traditional one. As such a distinction is not greatly emphasized in the literature, the graphical fundamentals are described in detail, and an alternative terminology is proposed to separate some concepts. Additionally, a compact notation is adopted to integrate the representation’s metadata into the graphic itself.