1. A method for determining histogram density estimators for data samples, comprising: generating a set of all possible histogram shapes of exactly, or at most, or any finite subset of, any prescribed finite positive integer number or numbers of bins for a data sample via a histogram application on a target device with one or more processors, wherein the data sample is obtained from a data analysis application or from a pre-determined data source; exactly determining a supremum of a likelihood function of histogram densities for each histogram shape in the generated set of all possible histogram shapes, wherein the supremum is a statistical estimate that maximizes a likelihood function among a set of histogram density functions having a same histogram shape and is selected from a set of finitely many histogram shapes; and displaying a graphical histogram of the data sample corresponding to a maximum likelihood for a selected histogram shape or a selected set of histogram shapes using the determined supremum via a histogram application on a graphical user interface on the target device.