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A simulation-based approach to the study of coefficient of variation of Gompertz distribution under progressive first-failure censoring

Author

Listed:
  • Ahmed A. Soliman

    (Sohag University)

  • A. H. Abd Ellah

    (Sohag University)

  • N. A. Abou-Elheggag

    (Sohag University)

  • G. A. Abd-Elmougod

    (Sohag University)

Abstract

In applied statistics, the coefficient of variation is widely used. However, inference concerning the coefficient of variation of non-normal distributions are rarely reported. In this article, a simulation-based Bayesian approach is adopted to estimate the coefficient of variation (CV) under progressive first-failure censored data from Gompertz distribution. The sampling schemes such as, first-failure censoring, progressive type II censoring, type II censoring and complete sample can be obtained as special cases of the progressive first-failure censored scheme. The simulation-based approach will give us a point estimate as well as the empirical sampling distribution of CV. The joint prior density as a product of conditional gamma density and inverted gamma density for the unknown Gompertz parameters are considered. In addition, the results of maximum likelihood and parametric bootstrap techniques are also proposed. An analysis of a real life data set is presented for illustrative purposes. Results from simulation studies assessing the performance of our proposed method are included.

Suggested Citation

  • Ahmed A. Soliman & A. H. Abd Ellah & N. A. Abou-Elheggag & G. A. Abd-Elmougod, 2011. "A simulation-based approach to the study of coefficient of variation of Gompertz distribution under progressive first-failure censoring," Indian Journal of Pure and Applied Mathematics, Springer, vol. 42(5), pages 335-356, October.
    • Handle: RePEc:spr:indpam:v:42:y:2011:i:5:d:10.1007_s13226-011-0022-8
    DOI: 10.1007/s13226-011-0022-8
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    References listed on IDEAS

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    1. Pang, Wan Kai & Yu, Bosco Wing-Tong & Troutt, Marvin D. & Hou, Shui Hung, 2008. "A simulation-based approach to the study of coefficient of variation of dividend yields," European Journal of Operational Research, Elsevier, vol. 189(2), pages 559-569, September.
    2. Mohan L. Garg & B. Raja Rao & Carol K. Redmond, 1970. "Maximum‐Likelihood Estimation of the Parameters of the Gompertz Survival Function," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 19(2), pages 152-159, June.
    3. Reh, Wolfgang & Scheffler, Bernard, 1996. "Significance tests and confidence intervals for coefficients of variation," Computational Statistics & Data Analysis, Elsevier, vol. 22(4), pages 449-452, August.
    4. Pang, Wan-Kai & Leung, Ping-Kei & Huang, Wei-Kwang & Liu, Wei, 2005. "On interval estimation of the coefficient of variation for the three-parameter Weibull, lognormal and gamma distribution: A simulation-based approach," European Journal of Operational Research, Elsevier, vol. 164(2), pages 367-377, July.
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