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On a bounded bimodal two-sided distribution fitted to the Old-Faithful geyser data

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  • Donatella Vicari
  • Johan Ren� van Dorp

Abstract

In this paper, we shall develop a novel family of bimodal univariate distributions (also allowing for unimodal shapes) and demonstrate its use utilizing the well-known and almost classical data set involving durations and waiting times of eruptions of the Old-Faithful geyser in Yellowstone park. Specifically, we shall analyze the Old-Faithful data set with 272 data points provided in Dekking et al. [3]. In the process, we develop a bivariate distribution using a copula technique and compare its fit to a mixture of bivariate normal distributions also fitted to the same bivariate data set. We believe the fit-analysis and comparison is primarily illustrative from an educational perspective for distribution theory modelers, since in the process a variety of statistical techniques are demonstrated. We do not claim one model as preferred over the other.

Suggested Citation

  • Donatella Vicari & Johan Ren� van Dorp, 2013. "On a bounded bimodal two-sided distribution fitted to the Old-Faithful geyser data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 1965-1978, September.
    • Handle: RePEc:taf:japsta:v:40:y:2013:i:9:p:1965-1978
    DOI: 10.1080/02664763.2013.800036
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    1. Eilers, Paul H.C. & Borgdorff, M.W., 2007. "Non-parametric log-concave mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5444-5451, July.
    2. Atkinson, A.C. & Riani, M., 2007. "Exploratory tools for clustering multivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 272-285, September.
    3. Donatella Vicari & Johan Rene Van Dorp & Samuel Kotz, 2008. "Two-sided generalized Topp and Leone (TS-GTL) distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1115-1129.
    4. Samuel Kotz & Johan René van Dorp, 2010. "Generalized Diagonal Band Copulas with Two-Sided Generating Densities," Decision Analysis, INFORMS, vol. 7(2), pages 196-214, June.
    5. A. Azzalini & A.W. Bowman, 1990. "A Look at Some Data on the Old Faithful Geyser," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(3), pages 357-365, November.
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