The exponentiated lindley geometric distribution with applications


We introduce a new three-parameter lifetime distribution, the exponentiated Lindley geometric distribution, which exhibits increasing, decreasing, unimodal, and bathtub shaped hazard rates. We provide statistical properties of the new distribution, including shape of the probability density function, hazard rate function, quantile function, order statistics, moments, residual life function, mean deviations, Bonferroni and Lorenz curves, and entropies. We use maximum likelihood estimation of the unknown parameters, and an Expectation-Maximization algorithm is also developed to find the maximum likelihood estimates. The Fisher information matrix is provided to construct the asymptotic confidence intervals. Finally, two real-data examples are analyzed for illustrative purposes.


© 2019 by the authors. cc-by


Compounding, Expectation-Maximization algorithm, Geometric distribution, Lifetime distribution, Lindley distribution, Maximum likelihood estimation


Peng, B., Xu, Z., & Wang, M.. 2019. The exponentiated lindley geometric distribution with applications. Entropy, 21(5).