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Modified Beta Linear Exponential Distribution with Hydrologic Applications

Author

Listed:
  • Hassan S. Bakouch

    (Tanta University)

  • Abdus Saboor

    (Kohat University of Science & Technology)

  • Muhammad Nauman Khan

    (Kohat University of Science & Technology)

Abstract

In this paper, we introduce a flexible modified beta linear exponential (MBLE) distribution. Our motivation, besides others are there, dues to its ability in hydrology applications. We investigate a set of its statistical properties for supporting such applications, like moments, moment generating function, conditional moments, mean deviations, entropy, mean and variance (reversed) residual life and maximum likelihood estimators with observed information matrix. The distribution can accommodate both decreasing and increasing hazard rates as well as upside down bathtub and bathtub shaped hazard rates. Moreover, several distributions arise as special cases of the distribution. The MBLE distribution with others are fitted to two hydrology data sets. It is shown that, the MBLE distribution is the best fit among the compared distributions based on nine goodness-of-fit statistics among them the Corrected Akaike information criterion, Hannan–Quinn information criterion, Anderson–Darling and Kolmogorov–Smirnov p value. Consequently, some parameters of these data are obtained such as return level, conditional mean, mean deviation about the return level, risk of failure for designing hydraulic structures. Finally, we hope that this model will be able to attract wider applicability in hydrology and other life areas.

Suggested Citation

  • Hassan S. Bakouch & Abdus Saboor & Muhammad Nauman Khan, 2021. "Modified Beta Linear Exponential Distribution with Hydrologic Applications," Annals of Data Science, Springer, vol. 8(1), pages 131-157, March.
    • Handle: RePEc:spr:aodasc:v:8:y:2021:i:1:d:10.1007_s40745-019-00222-7
    DOI: 10.1007/s40745-019-00222-7
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    References listed on IDEAS

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    1. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2008. "A generalized modified Weibull distribution for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 450-462, December.
    2. Kundu, Debasis & Raqab, Mohammad Z., 2005. "Generalized Rayleigh distribution: different methods of estimations," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 187-200, April.
    3. 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.
    4. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    5. Simon Broadbent, 1958. "Simple Mortality Rates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 7(2), pages 86-95, June.
    6. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    7. Pundir, Sudesh & Arora, Sangeeta & Jain, Kanchan, 2005. "Bonferroni Curve and the related statistical inference," Statistics & Probability Letters, Elsevier, vol. 75(2), pages 140-150, November.
    8. Awulachew, Seleshi Bekele, 2008. "A review of hydrology, sediment and water resource use in the Blue Nile Basin," IWMI Working Papers H041833, International Water Management Institute.
    9. Singla, Neetu & Jain, Kanchan & Kumar Sharma, Suresh, 2012. "The Beta Generalized Weibull distribution: Properties and applications," Reliability Engineering and System Safety, Elsevier, vol. 102(C), pages 5-15.
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