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On testing the log-gamma distribution hypothesis by bootstrap

Author

Listed:
  • Eduardo Gutiérrez González
  • José Villaseñor Alva
  • Olga Panteleeva
  • Humberto Vaquera Huerta

Abstract

In this paper we propose two bootstrap goodness of fit tests for the log-gamma distribution with three parameters, location, scale and shape. These tests are built using the properties of this distribution family and are based on the sample correlation coefficient which has the property of invariance with respect to location and scale transformations. Two estimators are proposed for the shape parameter and show that both are asymptotically unbiased and consistent in mean-squared error. The test size and power is estimated by simulation. The power of the two proposed tests against several alternative distributions is compared to that of the Kolmogorov-Smirnov, Anderson-Darling, and chi-square tests. Finally, an application to data from a production process of carbon fibers is presented. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Eduardo Gutiérrez González & José Villaseñor Alva & Olga Panteleeva & Humberto Vaquera Huerta, 2013. "On testing the log-gamma distribution hypothesis by bootstrap," Computational Statistics, Springer, vol. 28(6), pages 2761-2776, December.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:6:p:2761-2776
    DOI: 10.1007/s00180-013-0427-4
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    References listed on IDEAS

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    1. N. Sreekumar & P. Thomas, 2007. "Estimation of the parameters of log-gamma distribution using order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(1), pages 115-127, July.
    2. Meintanis, Simos G. & Tsionas, Efthimios, 2010. "Testing for the generalized normal-Laplace distribution with applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3174-3180, December.
    3. Gomes, O. & Combes, C. & Dussauchoy, A., 2008. "Parameter estimation of the generalized gamma distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 955-963.
    4. Meintanis, Simos G., 2008. "A new approach of goodness-of-fit testing for exponentiated laws applied to the generalized Rayleigh distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2496-2503, January.
    5. Meintanis, Simos G., 2010. "Inference procedures for the Birnbaum-Saunders distribution and its generalizations," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 367-373, February.
    6. Koutrouvelis, Ioannis A. & Canavos, George C. & Meintanis, Simos G., 2005. "Estimation in the three-parameter inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1132-1147, June.
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