Histogram Ordering

Frequency histograms are ubiquitous, being practically used in any field of science. In this paper, we present a partial order for frequency and, to our knowledge, no kind has been yet defined. This is based on the stochastic discrete probability distributions and it invariance properties that make unique. First, model histogram as sequence bins associated with (or relative frequency) distribution. Then, consider two ordered if they defined same their respective stochastically ordered. The ordering can be easily spotted because cumulative distribution functions frequencies do not cross each other. Finally, bin associate representative value bin, holds all quasi-arithmetic means (such arithmetic, harmonic, geometric mean) values weighted by direction than are. Our theoretical study supported three experiments fields image processing, traffic flow, income