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Poisson–exponential distribution: different methods of estimation

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  • Giovani Carrara Rodrigues
  • Francisco Louzada
  • Pedro Luiz Ramos

Abstract

In this study, we present different estimation procedures for the parameters of the Poisson–exponential distribution, such as the maximum likelihood, method of moments, modified moments, ordinary and weighted least-squares, percentile, maximum product of spacings, Cramer–von Mises and the Anderson–Darling maximum goodness-of-fit estimators and compare them using extensive numerical simulations. We showed that the Anderson–Darling estimator is the most efficient for estimating the parameters of the proposed distribution. Our proposed methodology was also illustrated in three real data sets related to the minimum, average and the maximum flows during October at São Carlos River in Brazil demonstrating that the PE distribution is a simple alternative to be used in hydrological applications.

Suggested Citation

  • Giovani Carrara Rodrigues & Francisco Louzada & Pedro Luiz Ramos, 2018. "Poisson–exponential distribution: different methods of estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 128-144, January.
    • Handle: RePEc:taf:japsta:v:45:y:2018:i:1:p:128-144
    DOI: 10.1080/02664763.2016.1268571
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    References listed on IDEAS

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    1. Francisco Louzada-Neto & Vicente G. Cancho & Gladys D.C. Barriga, 2011. "The Poisson--exponential distribution: a Bayesian approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(6), pages 1239-1248, April.
    2. Francisco Louzada-Neto, 1999. "Polyhazard Models for Lifetime Data," Biometrics, The International Biometric Society, vol. 55(4), pages 1281-1285, December.
    3. Cancho, Vicente G. & Louzada-Neto, Franscisco & Barriga, Gladys D.C., 2011. "The Poisson-exponential lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 677-686, January.
    4. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
    5. Louzada, Francisco & Roman, Mari & Cancho, Vicente G., 2011. "The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2516-2524, August.
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    Cited by:

    1. Cesar Augusto Taconeli & Wagner Hugo Bonat, 2020. "On the performance of estimation methods under ranked set sampling," Computational Statistics, Springer, vol. 35(4), pages 1805-1826, December.

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