Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-12-28
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
In general, although some random variables such as wind speed, temperature, and load are known to have multimodal distributions, input or output random variables are considered to follow unimodal distributions without assessing the unimodality or multimodality of distributions from samples.
In uncertainty analysis, estimating unimodal distribution as multimodal distribution or vice versa can lead to erroneous analysis results.
Thus, whether a distribution is unimodal or multimodal must be assessed before the estimation of distributions.
In this paper, the bimodality coefficient (BC) and Hartigan’s dip statistic (HDS), which are representative methods for assessing multimodality, are introduced and compared.
Then, a combined HDS with BC method is proposed.
The proposed method has the advantages of both BC and HDS by using the skewness and kurtosis of samples as well as the dip statistic through a link function between the BC values in BC and significance level in HDS.
To verify the performance of the proposed method, statistical simulation tests were conducted to evaluate the multimodality for various unimodal, bimodal, and trimodal models.
The implementation of the proposed method to real engineering data is shown through case studies.
The results demonstrate that the proposed method is more accurate, robust, and reliable than the BC and original HDS alone.
American Psychological Association (APA)
Kang, Young-Jin& Noh, Yoojeong. 2019. Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-17.
https://search.emarefa.net/detail/BIM-1195769
Modern Language Association (MLA)
Kang, Young-Jin& Noh, Yoojeong. Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions. Mathematical Problems in Engineering No. 2019 (2019), pp.1-17.
https://search.emarefa.net/detail/BIM-1195769
American Medical Association (AMA)
Kang, Young-Jin& Noh, Yoojeong. Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-17.
https://search.emarefa.net/detail/BIM-1195769
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1195769