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A generalized binomial exponential 2 distribution: modeling and applications to hydrologic events

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  • A. Asgharzadeh
  • Hassan S. Bakouch
  • M. Habibi

Abstract

Developing statistical methods to model hydrologic events is always interesting for both statisticians and hydrologists, because of its importance in hydraulic structures design and water resource planning. Because of this, a flexible 3-parameter generalization of the exponential distribution is introduced based on the binomial exponential 2 (BE2) distribution [2]. The proposed distribution involving the exponential, gamma and BE2 distributions as submodels; and it exhibits decreasing, increasing and bathtub-shaped hazard rates, so it turns out to be quite flexible for analyzing non-negative real life data. Some statistical properties, parameters estimation and information matrix of the distribution are investigated. The proposed distribution, Gumbel, generalized Logistic and other distributions are utilized to model and fit two hydrologic data sets. The distribution is shown to be more appropriate to the data than the compared distributions using the selection criteria: average scaled absolute error, Akaike information criterion, Bayesian information criterion and Kolmogorov–Smirnov statistics. As a result, some hydrologic parameters of the data are obtained such as return level, conditional mean, mean deviation about the return level and the rth moments of order statistics.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:13:p:2368-2387
    DOI: 10.1080/02664763.2016.1254729
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    References listed on IDEAS

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    1. Silva, Rodrigo B. & Barreto-Souza, Wagner & Cordeiro, Gauss M., 2010. "A new distribution with decreasing, increasing and upside-down bathtub failure rate," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 935-944, April.
    2. Barreto-Souza, Wagner & Cribari-Neto, Francisco, 2009. "A generalization of the exponential-Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2493-2500, December.
    3. Lemonte, Artur J. & Cordeiro, Gauss M., 2011. "The exponentiated generalized inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 506-517, April.
    4. Kang, Dongbum & Ko, Kyungnam & Huh, Jongchul, 2015. "Determination of extreme wind values using the Gumbel distribution," Energy, Elsevier, vol. 86(C), pages 51-58.
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    Cited by:

    1. Muhammad H. Tahir & Muhammad Adnan Hussain & Gauss M. Cordeiro & M. El-Morshedy & M. S. Eliwa, 2020. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension," Mathematics, MDPI, vol. 8(11), pages 1-28, November.
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    3. Mohamed S. Eliwa & Muhammad H. Tahir & Muhammad A. Hussain & Bader Almohaimeed & Afrah Al-Bossly & Mahmoud El-Morshedy, 2023. "Univariate Probability-G Classes for Scattered Samples under Different Forms of Hazard: Continuous and Discrete Version with Their Inferences Tests," Mathematics, MDPI, vol. 11(13), pages 1-24, June.

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