The beta compound Rayleigh distribution : Properties and applications

  • Authors

    • Hesham Reyad Assistant of professor in Qassim university
    • Soha Ibrahim assistant of professor in cairo university
    2017-05-30
    https://doi.org/10.14419/ijasp.v5i1.7513
  • Beta Distribution, Compound Rayleigh Distribution, Maximum Likelihood Estimation, Order Statistics, Record Statistics.

  • In this paper, we introduce a new four parameter continuous model, called the beta compound Rayleigh (BCR) distribution that extends the compound Rayleigh distribution. Basic properties of the proposed distribution such as; mean, variance, coefficient of variation, raw and incomplete moments, skewness, kurtosis, moment and probability generating functions, reliability analysis, Lorenz, Bonferroni and Zenga curves, Rényi of entropy, order statistics and record statistics are investigated. We obtain the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the usefulness of the new model.

  • References

    1. [1] T.A. Abushal, Estimation of the unknown parameters for the compound Rayleigh distribution based on progressive first-failure-censored sampling, Open Journal of Statistics, 1 (2011) 161-171. https://doi.org/10.4236/ojs.2011.13020.

      [2] O. Shajaee, R. Azimi and M. Babanezhad, Empirical Bayes estimators of parameter and reliability function for compound Rayleigh distribution under record data,American Journal of Theoretical andApplied Statistics, 1 (2012) 12-15.

      [3] D.R. Barot, and M.N. Patal, Performance of estimates of reliability parameters for compound Rayleigh progressive type-ii censored data, Control Theory and Informatics, 5 (2015) 33-41.

      [4] G.A. Abd-Elmougod, and E.E. Mahmoud, Parameters estimation of compound Ratleigh distribution under an adaptive type-ii progressive hybrid censored data for constant partially accelerated life tests. Global Journal of Pure and Applied Mathematics, 12(2016) 3253-3273.

      [5] N. Eugene, C. Lee, F. Famoye, The beta-normal distribution and its applications,Communication in Statistics-Theory and Methods, 31(2002) 497-512. https://doi.org/10.1081/STA-120003130.

      [6] C. Kleiber, S.Kotz, Statistical Size Distributions in Economics and Actuarial Sciences, Wiley Series in Probability and Statistics. John Wily & Sons, 2003

      [7] B.O. Oluyede, S. Rajasooriya, The Mc-Dagum distribution and its statistical properties with applications,Asian Journal of Mathematics and Applications, 44(2013) 1-16.

      [8] M. Ahsanullah,Record Statistics. New York: Nova Science Publishers, Inc. Commack, 1995.

      [9] B.C. Arnold, N. Balakrishan, H.N. Nagaraja,Records. New York, Wiley, USA, 1998.

      [10] R.L. Smith, J.C. Naylor, A comparison of maximum likelihood estimators for the three-parameter Weibull distribution, Appl Stat, 36(1987) 358:369.

      [11] F. Merovci, M.A.Khaleel, N.A., Ibrahim, M. Shitan, The beta Burr type x distribution properties with applications, Springer Plus, 5(2016):697.doi: 10.1186/s40064-016-2271-9. eCollection 2016

      [12] A.J. Gross, V. A. Clark, Survival distributions: Reliability applications in the binomial sciences, John Wiley and Sons, New York, 1975

      [13] J.A. Rodrigues, A.P.C. Silva, G.G. Hamedani, The beta exponential Lindley distribution, Journalof Statistical Theory and Applications, 14(2014):60-75. https://doi.org/10.2991/jsta.2015.14.1.6.

      [14] M.E. Mead, On five- parameter Lomax distribution: properties and applications,PakistanJournal of Statistics and Operations Research, 1(2016) 185-199.

      [15] F. Merovci, Transmuted generalized Rayleigh distribution, AJ. Stat. Appl, 3, 1(2014):9-20.

      [16] A.Z. Afify, ZM. Nofal, A.E. Ebraheim, Exponential transmuted generalized Rayleigh distribution: A new four parameter Rayleigh distribution, Pakistan Journal of Statistics and Operations Research, XI,1(2015) 115-134. https://doi.org/10.18187/pjsor.v11i1.873.

  • Downloads

    Additional Files