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

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 ar...

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Published inAlphanumeric journal Vol. 4; no. 2; pp. 1 - 10
Main Authors KÖYMEN KESER, İstem, DEVECİ KOCAKOÇ, İpek, ŞEHİRLİOĞLU, Ali Kemal
Format Journal Article
LanguageEnglish
Published Istanbul University 23.09.2016
Subjects
coefficient of variation function
descriptive statistics
functional data analysis
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Summary: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 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.
ISSN:2148-2225
2148-2225
DOI:10.17093/aj.2016.4.2.5000185408