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

Ahmed A. Soliman (), A. H. Abd Ellah, N. A. Abou-Elheggag and G. A. Abd-Elmougod
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Ahmed A. Soliman: Sohag University
A. H. Abd Ellah: Sohag University
N. A. Abou-Elheggag: Sohag University
G. A. Abd-Elmougod: Sohag University

Indian Journal of Pure and Applied Mathematics, 2011, vol. 42, issue 5, 335-356

Abstract: 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.

Keywords: Coefficient of variation; Gompertz distribution; Progressive first-failure censored scheme; Bayesian and non-Bayesian approaches; Gibbs and Metropolis sampler; Bootstrap method (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s13226-011-0022-8

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