Cumulative triangle for visual analysis of empirical data

Purpose. The development of a graphical object for visual analysis that allows for simultaneous evaluation of both general characteristics and details of the empirical data distribution. Methodology. Justification of the feasibility and sequence of creating the cumulative triangle, as well as proving its properties, was carried out using geometric constructions, generalization, and lattice functions. The construction of the cumulative triangle was implemented in the “Matlab” software. Samples of random variables with known distribution laws were obtained using a pseudo-random number generator. Previously calculated dependencies of the spectral power density of seismic-acoustic noise-like signals were used as empirical data. Findings. A folded cumulative function of the n-th order was introduced as a generalization of the known folded cumulative function. Using the folded cumulative functions, a geometric object that is the cumulative triangle, was designed to visualize the empirical distribution function. Lines dividing the triangle into flat curvilinear quadrilaterals are plotted on each triangle. It is shown that the face area can be used as a characteristic of the random variable concentration near the abscissa of the face upper node, and the difference in the areas of the face left and right parts provides for assessing the asymmetry of the distribution over the interval covering the face. Originality. A new graphical object for visual analysis of empirical data distribution is proposed. It is shown how, relying on its appearance, conclusions can be drawn both regarding the characteristics of the entire sample and individual intervals of the distribution function. Practical value. The cumulative triangle can be a useful addition to graphical visualization tools. Its use allows for simultaneous detailing and generalization of the properties of experimentally obtained data at different scale levels, which is particularly valuable when data have complicated and variable distributions.