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

What is it about?

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 the 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 are reported on a well-known 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. Keywords: Coefficient Of Variation Function, Descriptive Statistics, Functional Data Analysis

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Photo by Web Hosting on Unsplash

Why is it important?

Our aim in this paper is to propose a new descriptive statistic, “coefficient of variation” for functional data. Although standard deviation function and mean function themselves are not new, a new concept of coefficient variation (CV) function is necessary to compare the variation between curve groups especially when the mean curves are different between curve groups.

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