Averaged shifted histograms (ASHs) or weighted averaging of rounded points (WARPs): Efficient methods to calculate kernel density estimators for circular data

By solving the histograms' problems of origin dependency and discontinuity and by having guidance to choose the best bandwidth and the feasibility of variable bandwidth procedures, the kernel density estimators (KDEs) are powerful tools to explore and analyze data distributions. However, an important drawback of these methods is that they require a considerable number of calculations, which may require a long time to obtain the result, even using fast processors and moderate sample sizes. A way to overcome this problem is through ASHs, a procedure later recognized as being a part of the more general procedure. On the other hand, the information with a circular measure scale commonly occurs in diverse human activities. Circular data distribution must be understood to properly interpret its message. The rose diagram is the histogram equivalent, sharing the same drawbacks along with others derived from the circular scale. In this talk, I present a new program that permits the calculation of kernel density estimators for circular data with different weight functions by means of the ASH-WARP procedure with an impressive calculation time (from minutes to less than a second) when analyzing big datasets.