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Modelling skewness and kurtosis with the BCPE density in GAMLSS

Author

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  • Vlasios Voudouris
  • Robert Gilchrist
  • Robert Rigby
  • John Sedgwick
  • Dimitrios Stasinopoulos

Abstract

This paper illustrates the power of modern statistical modelling in understanding processes characterised by data that are skewed and have heavy tails. Our particular substantive problem concerns film box-office revenues. We are able to show that traditional modelling techniques based on the Pareto--Levy--Mandelbrot distribution led to what is actually a poorly supported conclusion that these data have infinite variance. This in turn led to the dominant paradigm of the movie business that ‘nobody knows anything’ and hence that box-office revenues cannot be predicted. Using the Box--Cox power exponential distribution within the generalized additive models for location, scale and shape framework, we are able to model box-office revenues and develop probabilistic statements about revenues.

Suggested Citation

  • Vlasios Voudouris & Robert Gilchrist & Robert Rigby & John Sedgwick & Dimitrios Stasinopoulos, 2012. "Modelling skewness and kurtosis with the BCPE density in GAMLSS," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1279-1293, November.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:6:p:1279-1293
    DOI: 10.1080/02664763.2011.644530
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    References listed on IDEAS

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    Cited by:

    1. Thiago G. Ramires & Niel Hens & Gauss M. Cordeiro & Edwin M. M. Ortega, 2018. "Estimating nonlinear effects in the presence of cure fraction using a semi-parametric regression model," Computational Statistics, Springer, vol. 33(2), pages 709-730, June.
    2. Voudouris, Vlasios & Ayres, Robert & Serrenho, Andre Cabrera & Kiose, Daniil, 2015. "The economic growth enigma revisited: The EU-15 since the 1970s," Energy Policy, Elsevier, vol. 86(C), pages 812-832.
    3. Silvia L. P. Ferrari & Giovana Fumes, 2017. "Box–Cox symmetric distributions and applications to nutritional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(3), pages 321-344, July.
    4. Fernanda De Bastiani & Robert A. Rigby & Dimitrios M. Stasinopoulous & Audrey H.M.A. Cysneiros & Miguel A. Uribe-Opazo, 2018. "Gaussian Markov random field spatial models in GAMLSS," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 168-186, January.
    5. Rigby, Robert & Stasinopoulos, Dimitrios & Voudouris, Vlasios, 2015. "Flexible statistical models: Methods for the ordering and comparison of theoretical distributions," MPRA Paper 63620, University Library of Munich, Germany.
    6. Giovana Fumes-Ghantous & Silvia L. P. Ferrari & José Eduardo Corrente, 2018. "Box–Cox t random intercept model for estimating usual nutrient intake distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 715-734, December.
    7. Raúl Alejandro Morán-Vásquez & Silvia L. P. Ferrari, 2019. "Box–Cox elliptical distributions with application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(5), pages 547-571, July.
    8. Ayres, Robert & Voudouris, Vlasios, 2014. "The economic growth enigma: Capital, labour and useful energy?," Energy Policy, Elsevier, vol. 64(C), pages 16-28.
    9. Naderi, Mehrdad & Hashemi, Farzane & Bekker, Andriette & Jamalizadeh, Ahad, 2020. "Modeling right-skewed financial data streams: A likelihood inference based on the generalized Birnbaum–Saunders mixture model," Applied Mathematics and Computation, Elsevier, vol. 376(C).

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