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Two New Mixture Models Related to the Inverse Gaussian Distribution

Author

Listed:
  • Samuel Kotz

    (The George Washington University)

  • Víctor Leiva

    (Universidad de Valparaíso)

  • Antonio Sanhueza

    (Universidad de La Frontera)

Abstract

This article presents a new family of logarithmic distributions to be called the sinh mixture inverse Gaussian model and its associated life distribution referred as the extended mixture inverse Gaussian model. Specifically, the density, distribution function, and moments are developed for the sinh mixture inverse Gaussian distribution. Next, the extended mixture inverse Gaussian distribution is characterized. A graphical analysis of the densities of the new models is also provided. In addition, a lifetime analysis is presented for the extended mixture inverse Gaussian distribution. Finally, an example with a real data set is given to illustrate the methodology, which indicates that the new models result in a better fit to the data than some other well-known distributions.

Suggested Citation

  • Samuel Kotz & Víctor Leiva & Antonio Sanhueza, 2010. "Two New Mixture Models Related to the Inverse Gaussian Distribution," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 199-212, March.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:1:d:10.1007_s11009-008-9112-4
    DOI: 10.1007/s11009-008-9112-4
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Adriano Suzuki & Vicente Cancho & Francisco Louzada, 2016. "The Poisson–Inverse-Gaussian regression model with cure rate: a Bayesian approach and its case influence diagnostics," Statistical Papers, Springer, vol. 57(1), pages 133-159, March.
    2. Fernando Rojas & Peter Wanke & Víctor Leiva & Mauricio Huerta & Carlos Martin-Barreiro, 2022. "Modeling Inventory Cost Savings and Supply Chain Success Factors: A Hybrid Robust Compromise Multi-Criteria Approach," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    3. Kelmansky Diana M. & Martínez Elena J. & Leiva Víctor, 2013. "A new variance stabilizing transformation for gene expression data analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 12(6), pages 653-666, December.
    4. Danilo Leal & Rodrigo Jiménez & Marco Riquelme & Víctor Leiva, 2023. "Elliptical Capital Asset Pricing Models: Formulation, Diagnostics, Case Study with Chilean Data, and Economic Rationale," Mathematics, MDPI, vol. 11(6), pages 1-27, March.
    5. Robert G. Aykroyd & Víctor Leiva & Carolina Marchant, 2018. "Multivariate Birnbaum-Saunders Distributions: Modelling and Applications," Risks, MDPI, vol. 6(1), pages 1-25, March.
    6. Jimmy Reyes & Jaime Arrué & Víctor Leiva & Carlos Martin-Barreiro, 2021. "A New Birnbaum–Saunders Distribution and Its Mathematical Features Applied to Bimodal Real-World Data from Environment and Medicine," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    7. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "Multivariate Skew-Normal Generalized Hyperbolic distribution and its properties," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 73-85.
    8. Helton Saulo & Roberto Vila & Giovanna V. Borges & Marcelo Bourguignon & Víctor Leiva & Carolina Marchant, 2023. "Modeling Income Data via New Parametric Quantile Regressions: Formulation, Computational Statistics, and Application," Mathematics, MDPI, vol. 11(2), pages 1-25, January.
    9. Azevedo, Cecilia & Leiva, Víctor & Athayde, Emilia & Balakrishnan, N., 2012. "Shape and change point analyses of the Birnbaum–Saunders-t hazard rate and associated estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3887-3897.

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