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Copula analysis of mixture models

Author

Listed:
  • M. Vrac
  • L. Billard
  • E. Diday
  • A. Chédin

Abstract

Contemporary computers collect databases that can be too large for classical methods to handle. The present work takes data whose observations are distribution functions (rather than the single numerical point value of classical data) and presents a computational statistical approach of a new methodology to group the distributions into classes. The clustering method links the searched partition to the decomposition of mixture densities, through the notions of a function of distributions and of multi-dimensional copulas. The new clustering technique is illustrated by ascertaining distinct temperature and humidity regions for a global climate dataset and shows that the results compare favorably with those obtained from the standard EM algorithm method. Copyright Springer-Verlag 2012

Suggested Citation

  • M. Vrac & L. Billard & E. Diday & A. Chédin, 2012. "Copula analysis of mixture models," Computational Statistics, Springer, vol. 27(3), pages 427-457, September.
    • Handle: RePEc:spr:compst:v:27:y:2012:i:3:p:427-457
    DOI: 10.1007/s00180-011-0266-0
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    References listed on IDEAS

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    1. Gildas Brossier, 1990. "Piecewise hierarchical clustering," Journal of Classification, Springer;The Classification Society, vol. 7(2), pages 197-216, September.
    2. Celeux, Gilles & Govaert, Gerard, 1992. "A classification EM algorithm for clustering and two stochastic versions," Computational Statistics & Data Analysis, Elsevier, vol. 14(3), pages 315-332, October.
    3. Phipps Arabie & J. Carroll, 1980. "Mapclus: A mathematical programming approach to fitting the adclus model," Psychometrika, Springer;The Psychometric Society, vol. 45(2), pages 211-235, June.
    4. Ali, Mir M. & Mikhail, N. N. & Haq, M. Safiul, 1978. "A class of bivariate distributions including the bivariate logistic," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 405-412, September.
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    Citations

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    Cited by:

    1. Francisco de A. T. Carvalho & Antonio Irpino & Rosanna Verde & Antonio Balzanella, 2022. "Batch Self-Organizing Maps for Distributional Data with an Automatic Weighting of Variables and Components," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 343-375, July.
    2. Sri Winarni & Sapto Wahyu Indratno & Restu Arisanti & Resa Septiani Pontoh, 2024. "Image Feature Extraction Using Symbolic Data of Cumulative Distribution Functions," Mathematics, MDPI, vol. 12(13), pages 1-17, July.
    3. Mazo, Gildas, 2016. "A semiparametric and location-shift copula-based mixture model," LIDAM Discussion Papers ISBA 2016026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Lee, Sharon X. & McLachlan, Geoffrey J., 2022. "An overview of skew distributions in model-based clustering," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    5. Będowska-Sójka, Barbara & Echaust, Krzysztof, 2020. "What is the best proxy for liquidity in the presence of extreme illiquidity?," Emerging Markets Review, Elsevier, vol. 43(C).

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