Science Journal of Applied Mathematics and Statistics

| Peer-Reviewed |

Bayes Estimation of Topp-Leone Distribution Under Symmetric Entropy Loss Function Based on Lower Record Values

Received: 09 October 2016    Accepted: 20 October 2016    Published: 14 November 2016
Views:       Downloads:

Share This Article

Abstract

This paper will study the estimation of parameter of Topp-Leone distribution based on lower record values. First, the minimum variance unbiased estimator and maximum likelihood estimator are obtained. Then the Bayes estimator is derived under symmetric loss function and further the empirical Bayes estimators is also obtained based on marginal probability density of record sample and maximum likelihood method. Finally, the admissibility and inadmissibility of a generally class of inverse linear estimators are also discussed.

DOI 10.11648/j.sjams.20160406.16
Published in Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 6, December 2016)
Page(s) 284-288
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Admissibility, Bayes and Empirical Bayes Estimators, Record Values, Symmetric Entropy Loss Function

References
[1] Ghitany M. E., Kotz S., Xie M., 2005. On some reliability measures and their stochastic orderings for the Topp-Leone distribution. Journal of Applied Statistics, 32(7):715-722.
[2] Al-Zahrani B., 2012. Goodness-of-fit for the Topp-Leone distribution with unknown parameters. Applied Mathematical Sciences, (125-128):6355-6363.
[3] Sindhua T. N., Saleemb M., Aslama M., 2013. Bayesian Estimation for Topp-Leone Distribution under Trimmed Samples. Journal of Basic and Applied Scientific Research 3(10):347-360.
[4] Al-Zahrani B., Alshomrani A., 2012. Inference on stress-strength reliability from Topp-Leone distributions. Journal of King Abdulaziz University-Science, 24(1):73-88.
[5] Bayoud H. A., 2015. Estimating the shape parameter of the Topp–Leone distribution based on Type I censored samples. Applicationes Mathematicae, 42(2):219-230.
[6] Feroze N., Aslam M., Saleem M., 2013. Statistical properties of two component mixture of Topp Leone distribution under a Bayesian approach. International Journal of Intelligent Technologies & Applied Statistics, 6(3):403-404.
[7] El-Sayed M. A., Abd-Elmougod G. A., Abdel-Rahman E. O., 2015. Estimation for coefficient of variation of Topp-Leone distribution under adaptive Type-II progressive censoring scheme: Bayesian and non-Bayesian approaches. Journal of Computational & Theoretical Nanoscience, 12(11):4028-4035.
[8] El-Sayed M. A., Abd-Elmougod G. A., Abdel-Khalek S., et al., 2013. Bayesian and non-Bayesian estimation of Topp-Leone distribution based lower record values. 45(2):133-145.
[9] Chandler K. N., 1952. The distribution and frequency of record values, Journal of the Royal Statistical Society B, 14(2):220-228.
[10] Raqab M. Z., 2002. Inferences for generalized exponential distribution based on record statistics. Journal of Statistical Planning & Inference, 104(2):339-350.
[11] Soliman A. A, Ellah A. H. A., Sultan K. S., 2006. Comparison of estimates using record statistics from Weibull model: Bayesian and non-Bayesian approaches. Computational Statistics & Data Analysis, 51(3):2065-2077.
[12] Jaheen Z. F., 2003. A Bayesian analysis of record statistics from the Gompertz model. Applied Mathematics & Computation, 145(2):307-320.
[13] Ahmadi J., Doostparast M., Parsian A., 2005. Estimation and prediction in a two-parameter exponential distribution based on k-record values under LINEX loss function. Communication in Statistics-Theory and Methods, 34(4): 795-805.
[14] Amin E. A., 2012. Bayesian and non-Bayesian estimation from type I generalized logistic distribution based on lower record values, Journal of Applied Sciences Research, 2012(1):118-126.
[15] Selim M. A., 2012. Bayesian estimations from the two-parameter bathtub-shaped lifetime distribution based on record values, Pakistan Journal of Statistics & Operation Research, 8(2):155-165.
[16] Zakerzadeh H., Jafari A. A., 2015, Inference on the parameters of two Weibull distributions based on record values, Statistical Methods & Applications, 24(1):25-40.
[17] Arabi B. R., Arashi M., Tabatabaey S., 2014. Improved confidence intervals for the scale parameter of Burr XII model based on record values. Computational Statistics, 29(5): 1153-1173.
[18] Barranco-Chamorro I., Moreno-Rebollo J. L., Jiménez-Gamero M. D., Alba-Fernández M. V., 2015. Estimation of the sample size based on record values. Mathematics & Computers in Simulation, 55(118): 58-72.
[19] Algamal Z. Y., 2016. Using maximum likelihood ratio test to discriminate between the inverse Gaussian and Gamma distributions, International Journal of Statistical Distributions, 1 (1): 27-32.
[20] Du Y. J., Sun X. X., 2007. Estimation of scale parameter of normal distribution under q-Symmetric entropy loss function. Journal of Jilin University, 45(5):39-43.
[21] Bayoud H. A., 2015. Admissible minimax estimators for the shape parameter of Topp–Leone distribution. Communication in Statistics-Theory and Methods, 45(1):71-82.
[22] Zakerzadeh H., Zahraie S. H. M., 2015. Admissibility in non-regular family under squared-log error loss. Metrika, 78(2): 227-236.
[23] Cao, M. X., Kong, F. C., 2013. General admissibility for linear estimators in a general multivariate linear model under balanced loss function. Acta Mathematica Sinica, 29(29): 1823-1832.
[24] Arnold, B. C., Balakrishnan, N., Nagaraja, H. N., 1998. Records. New York: John Wiley & Sons.
[25] Zhao S., Song Y., Song L., et al., 2007. Estimation of ordered means of two sample exponential distributions under symmetric entropy loss. Journal of Jilin University, 45(1):44-48.
Author Information
  • Department of Basic Subjects, Hunan University of Finance and Economics, Changsha, China

Cite This Article
  • APA Style

    Lanping Li. (2016). Bayes Estimation of Topp-Leone Distribution Under Symmetric Entropy Loss Function Based on Lower Record Values. Science Journal of Applied Mathematics and Statistics, 4(6), 284-288. https://doi.org/10.11648/j.sjams.20160406.16

    Copy | Download

    ACS Style

    Lanping Li. Bayes Estimation of Topp-Leone Distribution Under Symmetric Entropy Loss Function Based on Lower Record Values. Sci. J. Appl. Math. Stat. 2016, 4(6), 284-288. doi: 10.11648/j.sjams.20160406.16

    Copy | Download

    AMA Style

    Lanping Li. Bayes Estimation of Topp-Leone Distribution Under Symmetric Entropy Loss Function Based on Lower Record Values. Sci J Appl Math Stat. 2016;4(6):284-288. doi: 10.11648/j.sjams.20160406.16

    Copy | Download

  • @article{10.11648/j.sjams.20160406.16,
      author = {Lanping Li},
      title = {Bayes Estimation of Topp-Leone Distribution Under Symmetric Entropy Loss Function Based on Lower  Record Values},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {4},
      number = {6},
      pages = {284-288},
      doi = {10.11648/j.sjams.20160406.16},
      url = {https://doi.org/10.11648/j.sjams.20160406.16},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.sjams.20160406.16},
      abstract = {This paper will study the estimation of parameter of Topp-Leone distribution based on lower record values. First, the minimum variance unbiased estimator and maximum likelihood estimator are obtained. Then the Bayes estimator is derived under symmetric loss function and further the empirical Bayes estimators is also obtained based on marginal probability density of record sample and maximum likelihood method. Finally, the admissibility and inadmissibility of a generally class of inverse linear estimators are also discussed.},
     year = {2016}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Bayes Estimation of Topp-Leone Distribution Under Symmetric Entropy Loss Function Based on Lower  Record Values
    AU  - Lanping Li
    Y1  - 2016/11/14
    PY  - 2016
    N1  - https://doi.org/10.11648/j.sjams.20160406.16
    DO  - 10.11648/j.sjams.20160406.16
    T2  - Science Journal of Applied Mathematics and Statistics
    JF  - Science Journal of Applied Mathematics and Statistics
    JO  - Science Journal of Applied Mathematics and Statistics
    SP  - 284
    EP  - 288
    PB  - Science Publishing Group
    SN  - 2376-9513
    UR  - https://doi.org/10.11648/j.sjams.20160406.16
    AB  - This paper will study the estimation of parameter of Topp-Leone distribution based on lower record values. First, the minimum variance unbiased estimator and maximum likelihood estimator are obtained. Then the Bayes estimator is derived under symmetric loss function and further the empirical Bayes estimators is also obtained based on marginal probability density of record sample and maximum likelihood method. Finally, the admissibility and inadmissibility of a generally class of inverse linear estimators are also discussed.
    VL  - 4
    IS  - 6
    ER  - 

    Copy | Download

  • Sections