Libby-Novick Kumaraswamy Distribution with Its Properties and Applications

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Abdul Saboor, Zafar Iqbal, Muhammad Hanif, Munir Ahmad, Libby-Novick Kumaraswamy Distribution with Its Properties and Applications, Int. J. Anal. Appl., 19 (3) (2021), 405-439.

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Abdul Saboor, Zafar Iqbal, Muhammad Hanif, Munir Ahmad

Abstract

The Kumaraswamy distribution is one of the most popular probability distributions with applications to real life data. In this paper, an extension of this distribution called the Libby-Novick Kumaraswamy (LNK) distribution is presented which is believed to provide greater flexibility to model scenarios involving skew-normal data than original one. Analytical expressions for various mathematical properties including its cdf, quantile function, moments, factorial moments, conditional momennts, moment generating function, characteristic function, vitality function, information generating function, reliability measures, mean deviations, mean residual function, Bonferroni and Lorenz Curves are derived.The parameters' estimation of LNK distribution is undertaken using the method of maximum likelihood estimation. A simulation study for different values of sample sizes, to assess the performance of the parameters of LNK distribution is provided.  For illustration and performance evaluation of LNK distribution three real-life data sets from the field of engineering and science adapted from earlier studies are used. On comparing the results to previously used methods, LNK distribution shows that it can give consistently better fit than other existing important lifetime models. It is found that the LNK distribution is more suitable and useful to study lifetime data.

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References

  1. Z. Iqbal, A. Saboor, M. Ahmad, A note on Libby-Novick Kumaraswamy distribution. Presented in 15th ISSOS conference (2017).
  2. D. L. Libby, M. R. Novick, Multivariate generalized beta distributions with applications to utility assessment. J. Educ. Stat. 7(4) (1982), 271-294.
  3. P. Kumaraswamy, A generalized probability density function for double-bounded random processes. J. Hydrol. 46(1-2) (1980), 79-88.
  4. M. C. Jones, Kumaraswamy's distribution: A beta-type distribution with some tractability advantages. Stat. Methodol. 6(1) (2009), 70-81.
  5. J. McDonald, Some generalized functions for the size distribution of income. Econometrica. 52(3) (1984), 647-665.
  6. P. A. Mitnik, New properties of the Kumaraswamy distribution. Commun. Stat., Theory Meth. 42(5) (2013), 741-755.
  7. J. J. Chen, M. R. Novick, Bayesian analysis for binomial models with generalized beta prior distributions. J. Educ. Stat. 9(2) (1984), 163-175.
  8. M. M. Ristić, B. V. Popović, S. Nadarajah, Libby and Novick's generalized beta exponential distribution. J. Stat. Comput. Simul. 85(4) (2013), 740-761.
  9. G. M. Cordeiro, L. H. de Santana, E. M. Ortega, R. R. Pescim, A new family of distributions: Libby-Novick beta. Int. J. Stat. Probab. 3(2) (2014), 63.
  10. M. Ali Ahmed, The new form Libby-Novick distribution, Communications in Statistics - Theory and Methods. 50 (2021), 540.
  11. M. Rashid, Z. Iqbal, M. Hanif, Characterizations and entropy measures of the libby-novick generalized beta distribution. Adv. Appl. Stat. 63(2) (2020), 235-259
  12. Z. Iqbal, M. Rashid, M. Hanif, Properties of the Libby-Novick generalized beta distribution with application. Int. J. Anal. Appl. 19 (2021), 360-388.
  13. G. M. Cordeiro, R. dos Santos Brito, The beta power distribution. Brazil. J. Probab. Stat. 26(1) (2012), 88-112.
  14. R. Dasgupta, On the distribution of burr with applications. Sankhya B, 73 (2011), 1-19.