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Abstract:
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In recent years, many statistician try to develop a new statistical distribution which has great flexibilities and can be fitted better to the complex data. In this paper, we intoduce the modified Weibull Geometric (MWG) distribution which generalizes the modified Weibull (MW) distribution in Lai et. al (2003). We find that he hazard function of the MWG distribution can be monotone increasin, decreasing or bathtub shaped. We derive the cumulative distribution, hazard functions and the density ofthe order statistics. In addition, we find that the expression for its moments and for the moments of the order statistics. Also, the expression of the Renyi entropy is provided. The maximum likelihood estimation procedure is discussed using EM algorithm. The Bayesian estimations are also obtained using Markov Chain Monte Carlo (MCMC) method. We obtain the information matrix of MWG distribution and discuss their inferences and model comparisons. Finally, one simulation study and two real data sets are considered to illustrate the flexibility and potentiality of the proposed distribution.
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