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A test for the geometric distribution based on linear regression of order statistics

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  • Jiménez-Gamero, M.D.
  • Alba-Fernández, M.V.

Abstract

This paper proposes and studies a novel test for the geometric distribution which is based on a characterization of that law in terms of the conditional expectation of the second order statistic, given the value of the first order statistic. The asymptotic null distribution of the test statistic and its limit under general conditions are derived, proving that it is consistent against fixed alternatives. It can also detect alternatives converging to the null at the rate n−1∕2, n denoting the sample size. A weighted bootstrap and a parametric bootstrap can be used to consistently estimate the null distribution. The finite sample performance of these two bootstrap approximations is assessed via simulation. The power of the new test is numerically compared with that of some existing tests, concluding that the proposal presents a competitive behavior.

Suggested Citation

  • Jiménez-Gamero, M.D. & Alba-Fernández, M.V., 2021. "A test for the geometric distribution based on linear regression of order statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 103-123.
    • Handle: RePEc:eee:matcom:v:186:y:2021:i:c:p:103-123
    DOI: 10.1016/j.matcom.2020.08.023
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    References listed on IDEAS

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    8. M. Jiménez-Gamero & A. Batsidis & M. Alba-Fernández, 2016. "Fourier methods for model selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 105-133, February.
    9. José González-Barrios & Federico O’Reilly & Raúl Rueda, 2006. "Goodness of Fit for Discrete Random Variables Using the Conditional Density," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(1), pages 77-94, August.
    10. Jiménez-Gamero, M. Dolores & Kim, Hyoung-Moon, 2015. "Fast goodness-of-fit tests based on the characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 172-191.
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