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The Exponentiated Lindley Geometric Distribution with Applications

by Bo Peng 1, Zhengqiu Xu 1 and Min Wang 2,*
1
School of Computer Science, Southwest Petroleum University, Chengdu 610500, China
2
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(5), 510; https://doi.org/10.3390/e21050510
Received: 4 April 2019 / Revised: 8 May 2019 / Accepted: 9 May 2019 / Published: 20 May 2019
(This article belongs to the Section Information Theory, Probability and Statistics)
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. View Full-Text
Keywords: compounding; Lindley distribution; geometric distribution; maximum likelihood estimation; Expectation-Maximization algorithm; lifetime distribution compounding; Lindley distribution; geometric distribution; maximum likelihood estimation; Expectation-Maximization algorithm; lifetime distribution
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Peng, B.; Xu, Z.; Wang, M. The Exponentiated Lindley Geometric Distribution with Applications. Entropy 2019, 21, 510.

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