Mathematical properties of the Kumaraswamy-Lindley distribution and its applications

  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract

    In this paper, a composite distribution of Kumaraswamy and Lindley distributions namely, Kumaraswamy-Lindley Kum-L distribution is introduced and studied. The Kum-L distribution generalizes sub-models for some widely known distributions. Some mathematical properties of the Kum-L such as hazard function, quantile function, moments, moment generating function and order statistics are obtained. Estimation of parameters for the Kum-L using maximum likelihood estimation and least square estimation techniques are provided. To illustrate the usefulness of the proposed distribution, simulation study and real data example are used.

  • Keywords

    Kumaraswamy Distribution; Lindley Distribution; Maximum Likelihood Estimation; Hazard Function; Order Statistics.

  • References

      [1] Ashour S. & Eltehiwy M. (2015) "Exponentiated power Lindley distribution". Journal of Advanced Research. 6, 895–905.

      [2] Bakouch, H., Al-Zaharani B., Al-Shomrani A., Marchi V. & Louzad F. (2012) "An extended Lindley distribution". Journal of the Korean Statistical Society. 41. 75 – 85.

      [3] Behairy S. M., AL-Dayian G. & EL-Helbawy A. (2016) "The Kumaraswamy-Burr Type III Distribution: Properties and Estimation". British Journal of Mathematics & Computer Science 14(2). 1-21.

      [4] Çakmakyapan S. &Kadılar G. (2014) "A New Customer Lifetime Duration Distribution: The Kumaraswamy Lindley Distribution". International Journal of Trade, Economics and Financ.5 (5). 441-444.

      [5] Cordeiro G. & Castro D. (2011). "A new family of generalized distributions". Journal of Statistical Computation and Simulation 81. 883-898.

      [6] Ghitany M., Al-Mutairi D., Balakrishnan N. & Al-Enezi L. (2013) "Power Lindley distribution and associated inference". Comput Stat Data Anal. 64. 20–33.

      [7] Ghitany M., Al-qallaf F., Al-Mutairi D. &Hussain H. (2011) "A two parameter weighted Lindley distribution and its applications to survival data". Math ComputSimulat. 81(6). 1190–1201.

      [8] Ghitany M., Atieh B. &Nadarajah S. (2008) "Lindley distribution and its application". Math Comput Simulat.78. 493–506.

      [9] Jones, M. (2004). "Families of distributions arising from distributions of order statistics (with discussion)". Test 13. 1-43.

      [10] Jorgensen B. (1982) "Statistical properties of the generalized inverse Gaussian distribution. New York: Springer-Verlag.

      [11] Lindley D. (1958) "Fiducial distributions and Bayes’ theorem". JR Stat. Soc. Ser. 20. 102–107.

      [12] Merovci F. &Elbatal I. (2014)"Transmuted Lindley-geometric and its application". J Stat Appl. 3(1). 77–91.

      [13] Nadarajah S., Bakouch H. &Tahmasbi R. (2011) "Generalized Lindley distribution". Sankhya. 73 (B). 331–59.

      [14] Salem, H. & selim, M. (2015). The Generalized Weibull-Exponential Distribution: Properties and Applications. International Journal of Statistics and Applications. 4(2): 102-112.

      [15] Sharma V., Singh S., Singh U. &Agiwal V. (2015) "The inverse Lindley distribution- A stress-strength reliability model with applications to head and neck cancer data. Journal of Industrial & Production Engineering. 32 (3). 162 – 173.

      [16] Swain J, Venkatraman S, Wilson J. (1988) "Least squares estimation of distribution function in Johnson’s translation system". J StatComputSimulat. 29. 271–97.




Article ID: 7410
DOI: 10.14419/ijasp.v5i1.7410

Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.