Startseite Marshall-Olkin Lindley-Log-logistic distribution: Model, properties and applications
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Marshall-Olkin Lindley-Log-logistic distribution: Model, properties and applications

  • Thatayaone Moakofi EMAIL logo , Broderick Oluyede und Boikanyo Makubate
Veröffentlicht/Copyright: 4. Oktober 2021
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

The authors introduce a new generalized distribution called the Marshall-Olkin Lindley-Log-logistic (MOLLLoG) distribution and discuss its distributional properties. The properties include hazard function, quantile function, moments, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of the order statistics and Rényi entropy. A Monte Carlo simulation study was used to examine the bias, relative bias and mean square error of the maximum likelihood estimators. The betterness of the new distribution compared to other distributions is illustrated by means of two real life datasets.

MSC 2010: 60E05; 62F10

Acknowledgement

The authors are grateful to the editor and referees for some very useful comments on an earlier version of this manuscript which led to this improved version.

  1. (Communicated by Gejza Wimmer)

References

[1] Afify, A. Z.—Cordeiro, G. M.—Yousof, H. M.—Saboor, A.—Ortega, E. M. M.: The Marshall-Olkin additive Weibull distribution with variable shapes for the hazard rate, Hacet. J. Math. Stat. 47(2), (2018), 365–381.Suche in Google Scholar

[2] Barlow, RE.—Towland, RH.—Freeman, T.: A Bayesian analysis of stress-rupture life of Kevlar 49/epoxy spherical pressure vessels, Proceedings of the Canadian Conference on Applied Statistics, 1984.Suche in Google Scholar

[3] Barreto-Souza, W.—Lemonte, A. J.—Cordeiro, G. M.: General results for the Marshall and Olkin family of distributions, An. Acad. Brasil. Ciénc. 85(1) (2013), 3–21.10.1590/S0001-37652013000100002Suche in Google Scholar

[4] Cordeiro, G. M.—Lemonte A. J. A.: On the Marshall-Olkin extended Weibull distribution, Statist. Papers 54 (2013), 333–353.10.1007/s00362-012-0431-8Suche in Google Scholar

[5] Chakraborty, S.—Handique, L.: The generalized Marshall-Olkin-Kumaraswamy-G family of distributions, J. Data Sci. 15(3) (2017), 391–422.10.6339/JDS.201707_15(3).0003Suche in Google Scholar

[6] Chambers, J.—Cleveland, W.—Kleiner, B.—Tukey, J.: Graphical Methods for Data Analysis, Chapman and Hall, London, 1983.Suche in Google Scholar

[7] Chen, G.—Balakrishnan, N.: A general purpose approximate goodness-of-fit test, J. Qual. Technol. 27 (1995), 154–161.10.1080/00224065.1995.11979578Suche in Google Scholar

[8] Ghitany, M. E—Al-Hussaini, E. K.—Al-Jarallah, R. A.: Marshall-Olkin extended Weibull distribution and its application to censored data, J. Appl. Stat. 32(10) (2005), 1025–1034.10.1080/02664760500165008Suche in Google Scholar

[9] Ghitany, M. E.—Atieh, B.—Nadarajah, S.: Lindley distribution and its applications, Math. Comput. Simulation 78(4) (2008), 493–506.10.1016/j.matcom.2007.06.007Suche in Google Scholar

[10] Ghitany, M. E—Al-Mutairi, D.—Balakrishnan, N.—Al-Enezi, I.: Power Lindley distribution and associated inference, Comput. Statist. Data Anal. 64 (2013), 20–33.10.1016/j.csda.2013.02.026Suche in Google Scholar

[11] Javed, M.—Nawaz, T.—Irfan M.: The Marshall-Olkin kappa distribution, J. King Saud Univ. Sci. 31(4) (2018), 684–691.10.1016/j.jksus.2018.01.001Suche in Google Scholar

[12] Krishna, E.—Jose, K. K.—Ristic, M. M.: Applications of Marshall-Olkin Fréchet distribution, Comm. Statist. Simul. Comput. 42(1) (2013) 76–89.10.1080/03610918.2011.633196Suche in Google Scholar

[13] Kumar, D.: Ratio and Inverse Moments of Marshall-Olkin Extended Burr Type III Distribution Based on Lower Generalized Order Statistics, J. Data Sci. 14(1) (2016), 53–66.10.6339/JDS.201601_14(1).0004Suche in Google Scholar

[14] Lee, E. T.—Wang, J. W.: Statistical Methods for Survival Data Analysis, 3rd Edition, John Wiley and Sons, New York, 2003.10.1002/0471458546Suche in Google Scholar

[15] Lazhar, B.: Marshall-Olkin Extended Generalized Gompertz Distribution, J. Data Sci. 15(2) (2017), 239–266.10.6339/JDS.201704_15(2).0004Suche in Google Scholar

[16] Lepetu, L.—Oluyede, B. O—Makubate, B.—Foya, S.—Mdlongwa, P.: Marshall-Olkin Log-Logistic extended Weibull distribution, J. Data Sci. 15(4) (2017), 691–722.10.6339/JDS.201710_15(4).00007Suche in Google Scholar

[17] Lindley, D. V.: Fiducial distributions and Bayes theorem, J. Royal Stat. Soc. Ser. B 20 (1958), 102–107.10.1111/j.2517-6161.1958.tb00278.xSuche in Google Scholar

[18] Marshall A. W.—Olkin I.: A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika 84 (1997), 641–652.10.1093/biomet/84.3.641Suche in Google Scholar

[19] Nadarajah, S.—Bakouch, H. S.—Tahmasbi, R.: A generalized Lindley distribution, Sankhya B 73 (2011), 331–359.10.1007/s13571-011-0025-9Suche in Google Scholar

[20] Oguntunde, P. E.—Balogun, O. S.—Okagbue, H. I.—Bishop, S. A.: The Weibull-exponential distribution: Its properties and applications, J. Appl. Sci. 15(11) (2015), 1305–1311.10.3923/jas.2015.1305.1311Suche in Google Scholar

[21] Oluyede, B. O.—Kenkwo, E.—Wandaku, D.: Lindley-log logistic distribution with applications, in preparation, (2020).10.16929/as/2020.2451.168Suche in Google Scholar

[22] Oluyede, B. O.—Yang, T.: A new class of generalized Lindley distributions with applications, J. Stat. Comput. Simul. 85(10), (2015), 2072–2100.10.1080/00949655.2014.917308Suche in Google Scholar

[23] Oluyede, B. O.—Yang, T.—Omolo, B.: A generalized class of Kumaraswamy Lindley distribution with applications to lifetime data, Journal of Computations & Modelling 5(1)(2015), 27–70.Suche in Google Scholar

[24] Rényi, A.: On measures of entropy and information, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, (1960), 547–561.Suche in Google Scholar

[25] Santos-Neto, M.—Bourguignon, M.—Zea, L. M.—Nascimento, A. D. C.: The Marshall-Olkin extended Weibull family of distributions, J. Stat. Distrib. Appl. 1(9) (2014), 1–9.10.1186/2195-5832-1-9Suche in Google Scholar

[26] Shanker, R.—Shukla, K. K.—Shanker, R.—Leonida, T. A.: A three-parameter Lindley distribution, Am. J. Math. Stat. 7(1) (2017), 15–26.Suche in Google Scholar

[27] Usman, R. M.—Haq, M. A. A. U.: The Marshall-Olkin extended inverted Kumaraswamy distribution, J. King Saud Univ. Sci. 32(1) (2018), 356–365.10.1016/j.jksus.2018.05.021Suche in Google Scholar

[28] Zakerzadeh, H.—Dolati, A.: Generalized Lindley distribution, J. Math. Ext. 3(2) (2009), 13–25.Suche in Google Scholar

[29] Zhang T.—Xie, M.: Comm. Statist. Simulation Comput. 36 (2007), 579–592.10.1080/03610910701236081Suche in Google Scholar

Received: 2020-07-14
Accepted: 2020-10-29
Published Online: 2021-10-04
Published in Print: 2021-10-26

© 2021 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. Regular papers
  2. Algebraic structures for pairwise comparison matrices: Consistency, social choices and Arrow’s theorem
  3. Polynomial functions on rings of dual numbers over residue class rings of the integers
  4. Sufficient conditions for p-valent functions
  5. Upper bounds for analytic summand functions and related inequalities
  6. Global structure for a fourth-order boundary value problem with sign-changing weight
  7. On the nonexistence conditions of solution of two-point in time problem for nonhomogeneous PDE
  8. Solvability of a nonlinear three-dimensional system of difference equations with constant coefficients
  9. Properties of critical and subcritical second order self-adjoint linear equations
  10. Korovkin type approximation via statistical e-convergence on two dimensional weighted spaces
  11. Approximation by a new sequence of operators involving Apostol-Genocchi polynomials
  12. Poisson like matrix operator and its application in p-summable space
  13. On the homological and algebraical properties of some Feichtinger algebras
  14. Disjoint topological transitivity for weighted translations generated by group actions
  15. On simultaneous limits for aggregation of stationary randomized INAR(1) processes with poisson innovations
  16. Marshall-Olkin Lindley-Log-logistic distribution: Model, properties and applications
  17. The shifted Gompertz-G family of distributions: Properties and applications
  18. On the testing hypothesis in uniform family of distributions with nuisance parameter
  19. Clarkson inequalities related to convex and concave functions
Heruntergeladen am 14.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2021-0052/html
Button zum nach oben scrollen