The Weibull-geometric distribution

作者：Souza Wagner Barreto; de Morais Alice Lemos; Cordeiro Gauss M^*

来源：Journal of Statistical Computation and Simulation, 2011, 81(5): 645-657.

DOI：10.1080/00949650903436554

• EM algorithm
• exponential distribution
• geometric distribution
• hazard function
• information matrix
• maximum likelihood estimation
• Weibull distribution

For the first time, we propose the Weibull-geometric (WG) distribution which generalizes the extended exponential-geometric (EG) distribution introduced by Adamidis et al. [K. Adamidis, T. Dimitrakopoulou, and S. Loukas, On a generalization of the exponential-geometric distribution, Statist. Probab. Lett. 73 (2005), pp. 259-269], the exponential-geometric distribution discussed by Adamidis and Loukas [K. Adamidis and S. Loukas, A lifetime distribution with decreasing failure rate, Statist. Probab. Lett. 39 (1998), pp. 35-42] and the Weibull distribution. We derive many of its standard properties. The hazard function of the EG distribution is monotone decreasing, but the hazard function of the WG distribution can take more general forms. Unlike the Weibull distribution, the new distribution is useful for modelling unimodal failure rates. We derive the cumulative distribution and hazard functions, moments, density of order statistics and their moments. We provide expressions for the Renyi and Shannon entropies. The maximum likelihood estimation procedure is discussed and an EM algorithm [A. P. Dempster, N.M. Laird, and D.B. Rubim, Maximum likelihood from incomplete data via the EM algorithm (with discussion), J.R. Stat. Soc. B 39 (1977), pp. 1-38; G.J. McLachlan and T. Krishnan, The EM Algorithm and Extension, Wiley, New York, 1997] is given for estimating the parameters. We obtain the observed information matrix and discuss inference issues. The flexibility and potentiality of the new distribution is illustrated by means of a real data set.

• 出版日期2011