IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i7p1042-d778631.html
   My bibliography  Save this article

On Generalizing Sarle’s Bimodality Coefficient as a Path towards a Newly Composite Bimodality Coefficient

Author

Listed:
  • Nicolae Tarbă

    (Computer Science and Engineering Department, Faculty of Automatic Control and Computers, Politehnica University of Bucharest, Splaiul Independenței 313, 060042 Bucharest, Romania
    These authors contributed equally to this work.)

  • Mihai-Lucian Voncilă

    (Computer Science and Engineering Department, Faculty of Automatic Control and Computers, Politehnica University of Bucharest, Splaiul Independenței 313, 060042 Bucharest, Romania
    These authors contributed equally to this work.)

  • Costin-Anton Boiangiu

    (Computer Science and Engineering Department, Faculty of Automatic Control and Computers, Politehnica University of Bucharest, Splaiul Independenței 313, 060042 Bucharest, Romania)

Abstract

Determining whether a distribution is bimodal is of great interest for many applications. Several tests have been developed, but the only ones that can be run extremely fast, in constant time on any variable-size signal window, are based on Sarle’s bimodality coefficient. We propose in this paper a generalization of this coefficient, to prove its validity, and show how each coefficient can be computed in a fast manner, in constant time, for random regions pertaining to a large dataset. We present some of the caveats of these coefficients and potential ways to circumvent them. We also propose a composite bimodality coefficient obtained as a product of the weighted generalized coefficients. We determine the potential best set of weights to associate with our composite coefficient when using up to three generalized coefficients. Finally, we prove that the composite coefficient outperforms any individual generalized coefficient.

Suggested Citation

  • Nicolae Tarbă & Mihai-Lucian Voncilă & Costin-Anton Boiangiu, 2022. "On Generalizing Sarle’s Bimodality Coefficient as a Path towards a Newly Composite Bimodality Coefficient," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1042-:d:778631
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/7/1042/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/7/1042/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jiang, R. & Murthy, D.N.P., 2011. "A study of Weibull shape parameter: Properties and significance," Reliability Engineering and System Safety, Elsevier, vol. 96(12), pages 1619-1626.
    2. Gregory Rozál & J. Hartigan, 1994. "The MAP test for multimodality," Journal of Classification, Springer;The Classification Society, vol. 11(1), pages 5-36, March.
    3. Felipe Gusmão & Edwin Ortega & Gauss Cordeiro, 2011. "The generalized inverse Weibull distribution," Statistical Papers, Springer, vol. 52(3), pages 591-619, August.
    4. Satheesh Kumar C & Manju L, 2017. "A Note on Logistic Mixture Distributions," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 2(5), pages 122-124, August.
    5. N. A. Rather & T. A. Rather, 2017. "New Generalizations of Exponential Distribution with Applications," Journal of Probability and Statistics, Hindawi, vol. 2017, pages 1-9, July.
    6. Cees Van Der Eijk, 2001. "Measuring Agreement in Ordered Rating Scales," Quality & Quantity: International Journal of Methodology, Springer, vol. 35(3), pages 325-341, August.
    7. Jin Wang & Michael R. Taaffe, 2015. "Multivariate Mixtures of Normal Distributions: Properties, Random Vector Generation, Fitting, and as Models of Market Daily Changes," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 193-203, May.
    8. Khalaf Ahmad & Zeinhum Jaheen & Heba Mohammed, 2011. "Finite mixture of Burr type XII distribution and its reciprocal: properties and applications," Statistical Papers, Springer, vol. 52(4), pages 835-845, November.
    9. Minxian Yang, 2008. "Normal log-normal mixture, leptokurtosis and skewness," Applied Economics Letters, Taylor & Francis Journals, vol. 15(9), pages 737-742.
    10. K. S. Sultan & A. S. Al-Moisheer, 2015. "Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-8, April.
    11. Rohatgi, Vijay K. & Székely, Gábor J., 1989. "Sharp inequalities between skewness and kurtosis," Statistics & Probability Letters, Elsevier, vol. 8(4), pages 297-299, September.
    12. Hossein Negarestani & Ahad Jamalizadeh & Sobhan Shafiei & Narayanaswamy Balakrishnan, 2019. "Mean mixtures of normal distributions: properties, inference and application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 501-528, May.
    13. P. M. Hartigan, 1985. "Computation of the Dip Statistic to Test for Unimodality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(3), pages 320-325, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Álvarez, Adolfo, 2013. "Recombining partitions via unimodality tests," DES - Working Papers. Statistics and Econometrics. WS ws130706, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Burman, Prabir & Polonik, Wolfgang, 2009. "Multivariate mode hunting: Data analytic tools with measures of significance," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1198-1218, July.
    3. Chacón, José E. & Fernández Serrano, Javier, 2024. "Bayesian taut splines for estimating the number of modes," Computational Statistics & Data Analysis, Elsevier, vol. 196(C).
    4. James Mitchell & Aubrey Poon & Dan Zhu, 2024. "Constructing density forecasts from quantile regressions: Multimodality in macrofinancial dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(5), pages 790-812, August.
    5. Suren Basov & Svetlana Danilkina & David Prentice, 2020. "When Does Variety Increase with Quality?," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 56(3), pages 463-487, May.
    6. Mariani, Fabio & Pérez-Barahona, Agustín & Raffin, Natacha, 2010. "Life expectancy and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 798-815, April.
    7. Dewan, Isha & Dijoux, Yann, 2015. "Modelling repairable systems with an early life under competing risks and asymmetric virtual age," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 215-224.
    8. Kyriaki Nanou & Galina Zapryanova & Fanni Toth, 2017. "An ever-closer union? Measuring the expansion and ideological content of European Union policy-making through an expert survey," European Union Politics, , vol. 18(4), pages 678-693, December.
    9. Deversi, Marvin & Ispano, Alessandro & Schwardmann, Peter, 2021. "Spin doctors: An experiment on vague disclosure," European Economic Review, Elsevier, vol. 139(C).
    10. Silvano Vergura, 2018. "A Statistical Tool to Detect and Locate Abnormal Operating Conditions in Photovoltaic Systems," Sustainability, MDPI, vol. 10(3), pages 1-15, February.
    11. Joerg Heining & Joerg Lingens, 2000. "Social Interaction in Regional Labour Markets," Regional and Urban Modeling 283600034, EcoMod.
    12. Lee, Sharon X. & McLachlan, Geoffrey J., 2022. "An overview of skew distributions in model-based clustering," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    13. Graham Elliott & Nikolay Kudrin & Kaspar Wüthrich, 2022. "Detecting p‐Hacking," Econometrica, Econometric Society, vol. 90(2), pages 887-906, March.
    14. Pfister, Roland & Wirth, Robert & Weller, Lisa & Foerster, Anna & Schwarz, Katharina, 2018. "Taking shortcuts: Cognitive conflict during motivated rule-breaking," MPRA Paper 95773, University Library of Munich, Germany.
    15. Pusch, Natasha, 2024. "Estimating the prevalence and frequency of adolescent substance use using zero-inflated models and variables associated with social learning, social bond, and opportunity," Journal of Criminal Justice, Elsevier, vol. 94(C).
    16. Adam, Klaus & Woodford, Michael, 2021. "Robustly optimal monetary policy in a new Keynesian model with housing," Journal of Economic Theory, Elsevier, vol. 198(C).
    17. Rasool Roozegar & Saralees Nadarajah & Eisa Mahmoudi, 2022. "The Power Series Exponential Power Series Distributions with Applications to Failure Data Sets," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 44-78, May.
    18. Ali Doostmoradi, 2018. "A New Distribution with two parameters to Lifetime Data," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 8(2), pages 30-35, September.
    19. John Ryter & Xinkai Fu & Karan Bhuwalka & Richard Roth & Elsa Olivetti, 2022. "Assessing recycling, displacement, and environmental impacts using an economics‐informed material system model," Journal of Industrial Ecology, Yale University, vol. 26(3), pages 1010-1024, June.
    20. Gauss Cordeiro & Cláudio Cristino & Elizabeth Hashimoto & Edwin Ortega, 2013. "The beta generalized Rayleigh distribution with applications to lifetime data," Statistical Papers, Springer, vol. 54(1), pages 133-161, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1042-:d:778631. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.