A New Descriptive Statistic for Functional Data: Functional Coefficient Of Variation

Abstract

In this study, we propose a new descriptive statistic, coefficient of variation function, for functional data analysis and present its utilization. We recommend coefficient of variation function, especially when we want to compare the variation of multiple curve groups and when the mean functions are different for each curve group. Besides, obtaining coefficient of variation functions in terms of cubic B-Splines enables the interpretation of the first and second derivative functions of these functions and provides a stronger inference for the original curves. The utilization and effects of the proposed statistic is reported on a wellknown data set from the literature. The results show that the proposed statistic reflects the variability of the data properly and this reflection gets clearer than that of the standard deviation function especially as mean functions differ.

Outlier detection based on the functional coefficient of variation

“…Classical descriptive statistics for univariate data can similarly be applied to functional data with minor modifications. If the variability of multiple functional data groups needs to be compared, especially when mean functions of these data groups are different, the coefficient of variation function can be used instead of the standard deviation function (Keser et al, 2016).…”

“…As denoted by Keser et al (2016), especially when the curves have a mean function very close to zero, the CV function gets affected. This should be considered as a drawback of the statistic itself and exists in the original CV concept.…”

“…Detailed information on descriptive statistics of functional data can be found in Shang (2015). Besides, Keser et al (2016) have discussed the coefficient of variation (CV) function, which is the functional equivalent of the coefficient of variation. Krzysko and Smaga (2019) examined the multivariate coefficient of variation for functional data as a value, not as a function.…”

A Capacity Management Tool for a Portfolio of Industrialization Projects

“…To understand the PjM allocation calculation, it is necessary to explain the concept of Coefficient of Variability (CV). This measure expresses the data variation regarding the average [19], as expressed in (8). After this value is calculated, it is identified whether the PjM allocation is representative or whether adjustments to the average PjM allocation are required.…”