Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions
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 uncer...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2019-01-01
|
Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2019/4819475 |
id |
doaj-ad320608782441b597917c23b8f41b0d |
---|---|
record_format |
Article |
spelling |
doaj-ad320608782441b597917c23b8f41b0d2020-11-25T02:37:04ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472019-01-01201910.1155/2019/48194754819475Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of DistributionsYoung-Jin Kang0Yoojeong Noh1Research Institute of Mechanical Technology, Pusan National University, Busan 609-735, Republic of KoreaSchool of Mechanical Engineering, Pusan National University, Busan 609-735, Republic of KoreaIn 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.http://dx.doi.org/10.1155/2019/4819475 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Young-Jin Kang Yoojeong Noh |
spellingShingle |
Young-Jin Kang Yoojeong Noh Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions Mathematical Problems in Engineering |
author_facet |
Young-Jin Kang Yoojeong Noh |
author_sort |
Young-Jin Kang |
title |
Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions |
title_short |
Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions |
title_full |
Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions |
title_fullStr |
Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions |
title_full_unstemmed |
Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions |
title_sort |
development of hartigan’s dip statistic with bimodality coefficient to assess multimodality of distributions |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2019-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2019/4819475 |
work_keys_str_mv |
AT youngjinkang developmentofhartigansdipstatisticwithbimodalitycoefficienttoassessmultimodalityofdistributions AT yoojeongnoh developmentofhartigansdipstatisticwithbimodalitycoefficienttoassessmultimodalityofdistributions |
_version_ |
1724796905487073280 |