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The beta generalized Pareto distribution with application to lifetime data

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  • Mahmoudi, Eisa

Abstract

The generalized Pareto (GP) distribution is useful in modeling extreme value data, because of its long tail feature. In this paper, a new generalized version of this distribution which is called the beta generalized Pareto (BGP) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the BGP distribution is provided. We give closed-form expressions for the density, cumulative distribution and hazard rate function. We derive the r th raw moment of this distribution. Moreover, we discuss estimation by the maximum likelihood and obtain an expression for Fisher’s information matrix. In the end, an application using three real data sets is presented.

Suggested Citation

  • Mahmoudi, Eisa, 2011. "The beta generalized Pareto distribution with application to lifetime data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(11), pages 2414-2430.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:11:p:2414-2430
    DOI: 10.1016/j.matcom.2011.03.006
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    References listed on IDEAS

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    1. Paranaíba, Patrícia F. & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R., 2011. "The beta Burr XII distribution with application to lifetime data," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1118-1136, February.
    2. Pescim, Rodrigo R. & Demétrio, Clarice G.B. & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Urbano, Mariana R., 2010. "The beta generalized half-normal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 945-957, April.
    3. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
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    Cited by:

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    2. Kousik Maiti & Suchandan Kayal, 2023. "Estimating Reliability Characteristics of the Log-Logistic Distribution Under Progressive Censoring with Two Applications," Annals of Data Science, Springer, vol. 10(1), pages 89-128, February.
    3. Nadarajah, Saralees & Rocha, Ricardo, 2016. "Newdistns: An R Package for New Families of Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i10).
    4. Halim Zeghdoudi & Lazri Nouara & Djabrane Yahia, 2018. "Lindley Pareto Distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 19(4), pages 671-692, December.
    5. Julia Adamska & Łukasz Bielak & Joanna Janczura & Agnieszka Wyłomańska, 2022. "From Multi- to Univariate: A Product Random Variable with an Application to Electricity Market Transactions: Pareto and Student’s t -Distribution Case," Mathematics, MDPI, vol. 10(18), pages 1-29, September.
    6. Badreddine Boumaraf & Nacira Seddik-Ameur & Vlad Stefan Barbu, 2020. "Estimation of Beta-Pareto Distribution Based on Several Optimization Methods," Mathematics, MDPI, vol. 8(7), pages 1-22, July.
    7. Neveka M. Olmos & Emilio Gómez-Déniz & Osvaldo Venegas, 2022. "The Heavy-Tailed Gleser Model: Properties, Estimation, and Applications," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    8. Elbatal I., 2013. "The Kumaraswamy Exponentiated Pareto Distribution," Stochastics and Quality Control, De Gruyter, vol. 28(1), pages 1-8, October.
    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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