The power inverse Lindley distribution: different methods of estimation

In the last years several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. For instance, Ghitany et al. (2013) proposed a new generalization of the Lindley distribution, called power Lindley distribution, whereas Sharma et al. (2015a) proposed the inverse Lindley distribution. From these two generalizations Barco et al. (2017) studied the inverse power Lindley distribution, also called by Sharma et al. (2015b) as generalized inverse Lindley distribution. Considering the inverse power Lindley distribution, in this paper is evaluate the performance, through Monte Carlo simulations, with respect to the bias and consistency of nine different methods of estimations (the maximum likelihood method and eight others based on the distance between the empirical and theoretical cumulative distribution function). The numerical results showed a better performance of the estimation method based on the Anderson-Darling test statistic. This conclusion is also observed in the analysis of two real data sets