alphanumeric journal
The Journal of Operations Research, Statistics, Econometrics and Management Information Systems
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 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
Jel Classification: C46
Fonksiyonel Veri İçin Yeni Bir Tanımlayıcı İstatistik: Fonksiyonel Değişkenlik Katsayısı
Öz
Bu çalışmada fonksiyonel veriler için yeni bir tanımlayıcı istatistik olan değişkenlik katsayısı fonksiyonunu önermekteyiz. Özellikle her bir eğri grubunun ortalama fonksiyonları farklı olduğu durumda, çoklu eğri gruplarının değişkenliklerini karşılaştırmada önerilen değişkenlik katsayısı fonksiyonunun kullanılmasını tavsiye ediyoruz. Değişkenlik katsayısı fonksiyonunu elde ederken kübik B-Splaynlar kullanıldığından dolayı, bu fonksiyonların birinci ve ikinci türev fonksiyonlarının da yorumlanabiliyor olması, orijinal eğriler hakkında daha güçlü çıkarımlar yapabilmemizi sağlamaktadır. Önerilen istatistiğin kullanımı ve etkileri literatürdeki iyi bilinen bir veri seti üzerinde raporlanmıştır. Sonuçlar göstermektedir ki önerilen istatistik verinin değişkenliğini düzgün bir şekilde yansıtmaktadır ve bu durum ortalama fonksiyonları farklılaştıkça standart sapma fonksiyonundan daha üstün bir hale gelmektedir.
Anahtar Kelimeler: Değişkenlik Katsayısı Fonksiyonu, Fonksiyonel Veri Analizi, Tanımlayıcı İstatistik
Suggested citation
(). A New Descriptive Statistic for Functional Data: Functional Coefficient of Variation. Alphanumeric Journal, 4(2), 1-10. http://dx.doi.org/10.17093/aj.2016.4.2.5000185408
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2016.04.02.ECON.01
alphanumeric journal
Pages 1-10
Received: April 13, 2016
Accepted: Aug. 11, 2016
Published: Sept. 26, 2016
2016 Köymen Keser, İ., Deveci Kocakoç, İ., Şehirlioğlu, AK.
This is an Open Access article, licensed under Creative Commons Attribution-NonCommercial 4.0 International License.
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