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The exponentiated generalized inverse Gaussian distribution

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  • Lemonte, Artur J.
  • Cordeiro, Gauss M.

Abstract

The modeling and analysis of lifetime data is an important aspect of statistical work in a wide variety of scientific and technological fields. Good (1953) introduced a probability distribution which is commonly used in the analysis of lifetime data. For the first time, based on this distribution, we propose the so-called exponentiated generalized inverse Gaussian distribution, which extends the exponentiated standard gamma distribution (Nadarajah and Kotz, 2006). Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters. The usefulness of the new model is illustrated by means of a real data set.

Suggested Citation

  • Lemonte, Artur J. & Cordeiro, Gauss M., 2011. "The exponentiated generalized inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 506-517, April.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:4:p:506-517
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    References listed on IDEAS

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    1. Truc T. Nguyen, 2003. "A proof of the conjecture on positive skewness of generalised inverse Gaussian distributions," Biometrika, Biometrika Trust, vol. 90(1), pages 245-250, March.
    2. H. M. Barakat & Y. H. Abdelkader, 2004. "Computing the moments of order statistics from nonidentical random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 13(1), pages 15-26, April.
    3. Barndorff-Nielsen, O. & Blæsild, P. & Halgreen, C., 1978. "First hitting time models for the generalized inverse Gaussian distribution," Stochastic Processes and their Applications, Elsevier, vol. 7(1), pages 49-54, March.
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    1. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
    2. Angelo Koudou & Christophe Ley, 2014. "Efficiency combined with simplicity: new testing procedures for Generalized Inverse Gaussian models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 708-724, December.
    3. Ziyad A. Alhussain & Essam A. Ahmed, 2020. "Estimation of exponentiated Nadarajah-Haghighi distribution under progressively type-II censored sample with application to bladder cancer data," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 631-657, June.
    4. Adebisi Ade Ogunde & Gbenga Adelekan Olalude & Oyebimpe Emmanuel Adeniji & Kayode Balogun, 2021. "Lehmann Type II Frechet Poisson Distribution: Properties, Inference and Applications as a Life Time Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-8, June.
    5. A. Asgharzadeh & Hassan S. Bakouch & M. Habibi, 2017. "A generalized binomial exponential 2 distribution: modeling and applications to hydrologic events," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2368-2387, October.
    6. Kousik Maiti & Suchandan Kayal & Aditi Kar Gangopadhyay, 2024. "On Progressively Censored Generalized X-Exponential Distribution: (Non) Bayesian Estimation with an Application to Bladder Cancer Data," Annals of Data Science, Springer, vol. 11(5), pages 1761-1798, October.
    7. Xiao Jiang & Saralees Nadarajah & Thomas Hitchen, 2024. "A Review of Generalized Hyperbolic Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 595-624, July.

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