Estimation and prediction for the Kumaraswamy-inverse Rayleigh distribution based on records

  • Authors

    • Mohamed Hussian Cairo university, Giza, Egypt
    • Essam A. Amin
    2014-02-04
    https://doi.org/10.14419/ijasp.v2i1.1729

  • Abstract

    In this paper, estimators for the parameters of the Kumaraswamy-inverse Rayleigh distribution based on record values are obtained. These estimators are derived using the maximum likelihood and Bayesian methods. The Bayesian estimators are derived under the well-known squared error (SE) loss function. Prediction of the future sth record value is derived using the maximum likelihood and Bayesian methods. Simulation study is conduct to illustrate the findings.

     

    Keywords: Kumaraswamy, Inverse Rayleigh, record values, Bayes estimator, squared error loss function prediction of future record values, Bayes estimation; maximum likelihood.

  • References

    1. K.N. Chandler, “The distribution and frequency of record values”, J. R. Stat. Soc. Ser. B 14(2), 220–228, 1952.
    2. M. Ahsanullah, “Linear prediction of record values for the two parameter exponential distribution”. Annals of the Institute of Statistical Mathematics, 32, 363-368, 1980.
    3. M. Ahsanullah, “Introduction to Record Values”. Ginn Press, Needham Heights, Massachusetts, 1988.
    4. M. Ahsanullah, “Estimation of the parameters of the Gumbel distribution based on the m record values”. Computational Statistics Quarterly, 3, 231-239, 1990.
    5. M. Ahsanullah, “Record values. The Exponential Distribution: Theory, Methods and Applications”, eds. N. Balakrishnan and A. P. Basu, Gordon and Breach Publishers, Newark, New Jersey. 1995.
    6. B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja, “A First Course in Order Statistics”, John Wiley & Sons, New York, 1992.
    7. B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja), “Records”, John Wiley & Sons, New York, 1998.
    8. N. Balakrishnan, M. Ahsanullah, and P. S. Chan, “Relations for single and product moments of record values from Gumbel distribution”, Statistics and Probability Letters, 15, 223-227, 1992.
    9. N. Balakrishnan, and M. Ahsanullah, “Recurrence relations for single and product moments of record values from generalized Pareto distribution”, Communications in Statistics-Theory and Methods, 23, 2841-2852, 1994.
    10. N. Balakrishnan, and M. Ahsanullah, “Relations for single and product moments of record values from exponential distribution”, Journal of Applied Statistical Science, 2, 73-87, 1995.
    11. N. Balakrishnan, M. Ahsanullah, and P. S. Chan, “On the logistic record values and associated inference”, Journal of Applied Statistical Science, 2, 233-248. 1995.
    12. M. A. Selim, “Bayesian Estimations from the Two-Parameter Bathtub- Shaped Lifetime Distribution Based on Record Values”, 8(2), 155-165, 2012.
    13. M. Nadar, A. Papadopoulos and F. Kızılaslan, “Statistical analysis for Kumaraswamy’s distribution based on record data”, Stat Papers, 54(2), 335-369, 2013.
    14. M. Amini and N. Balakrishnan, “Nonparametric meta-analysis of independent samples of records”, Computational Statistics & Data Analysis, 66, 70-81, 2013.
    15. M. Juhas and V. Skrivankova, “Characterization of general classes of distributions based on independent property of transformed record values”, Applied Mathematics and Computation, 226, 44–50, 2014.
    16. N. Balakrishnan, P. S. Chan, and M. Ahsanullah, “Recurrence relations for moments of record values from generalized extreme value distribution”, Communications in Statistics-Theory and Methods, 22, 1471-1482, 1993.
    17. M. Q. Shahbaz, S. Shahbaz and N. S. Butt, “The Kumaraswamy-Inverse Weibull Distribution”, Pakistan journal of statistics and operation research, 8(3): 479-489, 2012.
    18. P. Basak and N. Balakrishnan, “Maximum likelihood prediction of future record statistic”, Mathematical and statistical methods in reliability. In: Lindquist BH, Doksun KA (eds) Series on quality, reliability and engineering statistics, World Scientific Publishing, Singapore, 7, 159–175, 2003.
    19. E. K. Al-Hussaini and Z. F. Jaheen, “Bayesian prediction bounds for the Burr Type XII failure model”, Commun Stat Theor Meth, 24, 1829–1842, 1995.
    20. P. Congdon, “Bayesian Statistical Modeling”, Wiley, New York, 2001.

  • Downloads

  • Received date: 2014-01-06

    Accepted date: 2014-01-28

    Published date: 2014-02-04