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On a Birnbaum–Saunders distribution arising from a non-homogeneous Poisson process

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  • Fierro, Raúl
  • Leiva, Víctor
  • Ruggeri, Fabrizio
  • Sanhueza, Antonio

Abstract

The Birnbaum–Saunders distribution is based on the asymptotic normality of a sum of random variables. We propose a new version of this distribution assuming that the number of terms of such a sum depends on a non-homogeneous Poisson process. The classical Birnbaum–Saunders distribution is obtained when a homogeneous Poisson process is considered.

Suggested Citation

  • Fierro, Raúl & Leiva, Víctor & Ruggeri, Fabrizio & Sanhueza, Antonio, 2013. "On a Birnbaum–Saunders distribution arising from a non-homogeneous Poisson process," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1233-1239.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:1233-1239
    DOI: 10.1016/j.spl.2012.12.018
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    References listed on IDEAS

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    1. Gilberto A. Paula & Víctor Leiva & Michelli Barros & Shuangzhe Liu, 2012. "Robust statistical modeling using the Birnbaum‐Saunders‐t distribution applied to insurance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(1), pages 16-34, January.
    2. Leiva, Víctor & Sanhueza, Antonio & Silva, Andrés & Galea, Manuel, 2008. "A new three-parameter extension of the inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 78(11), pages 1266-1273, August.
    3. Gómez, Héctor W. & Olivares-Pacheco, Juan F. & Bolfarine, Heleno, 2009. "An extension of the generalized Birnbaum-Saunders distribution," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 331-338, February.
    4. Vilca, Filidor & Santana, Lucia & Leiva, Víctor & Balakrishnan, N., 2011. "Estimation of extreme percentiles in Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1665-1678, April.
    5. V�ctor Leiva & Emilia Athayde & Cecilia Azevedo & Carolina Marchant, 2011. "Modeling wind energy flux by a Birnbaum--Saunders distribution with an unknown shift parameter," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2819-2838, February.
    6. Leiva, Victor & Barros, Michelli & Paula, Gilberto A. & Galea, Manuel, 2007. "Influence diagnostics in log-Birnbaum-Saunders regression models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5694-5707, August.
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