The exponentiated lindley geometric distribution with applications

Abstract

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.

Description

© 2019 by the authors. cc-by

Keywords

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

Citation

Peng, B., Xu, Z., & Wang, M.. 2019. The exponentiated lindley geometric distribution with applications. Entropy, 21(5). https://doi.org/10.3390/e21050510

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