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Related Experiment Video

Updated: Nov 27, 2025

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The Exponentiated Lindley Geometric Distribution with Applications.

Bo Peng¹, Zhengqiu Xu¹, Min Wang²

¹School of Computer Science, Southwest Petroleum University, Chengdu 610500, China.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

A new exponentiated Lindley geometric distribution is introduced, offering flexible hazard rate shapes. This statistical model provides comprehensive properties and estimation methods for lifetime data analysis.

Keywords:

Expectation-Maximization algorithm Lindley distribution compounding geometric distribution lifetime distribution maximum likelihood estimation

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Area of Science:

Statistics
Probability Theory
Reliability Engineering

Background:

Lifetime distributions are crucial for modeling event occurrences over time.
Existing distributions may not capture the complex failure patterns observed in real-world data.
The need for flexible distributions with diverse hazard rate behaviors is recognized.

Purpose of the Study:

Introduce a novel three-parameter lifetime distribution: the exponentiated Lindley geometric distribution.
Investigate the statistical properties of this new distribution, including its hazard rate, moments, and entropy.
Develop and apply estimation techniques for the distribution's parameters.

Main Methods:

Defined the exponentiated Lindley geometric distribution and analyzed its probability density and hazard rate functions.
Derived key statistical properties: quantile function, order statistics, moments, and residual life function.
Employed maximum likelihood estimation (MLE) and the Expectation-Maximization (EM) algorithm for parameter estimation.

Main Results:

The exponentiated Lindley geometric distribution demonstrates flexible hazard rate shapes (increasing, decreasing, unimodal, bathtub).
Comprehensive statistical properties were derived, including moments, mean deviations, and entropy measures.
Maximum likelihood estimates were obtained using both direct MLE and the EM algorithm, with Fisher information matrix for confidence intervals.

Conclusions:

The proposed exponentiated Lindley geometric distribution offers a valuable addition to the statistical toolkit for lifetime data.
Its flexibility in modeling various hazard rates makes it suitable for diverse applications in reliability and survival analysis.
The provided estimation methods and analyzed properties facilitate its practical implementation.