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Extended inverse Lindley distribution: properties and application.

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This study introduces a flexible new probability distribution for modeling upside-down bathtub lifetime data. The extended inverse Lindley distribution shows promise for analyzing real-world datasets like river flood levels.

Keywords:
Extended inverse Lindley distributionInverse Lindley distributionUpside-down bathtub lifetime data

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Area of Science:

  • Statistics
  • Probability Theory
  • Reliability Engineering

Background:

  • The inverse Lindley distribution is a useful model for certain lifetime data.
  • There is a need for more flexible distributions to capture complex lifetime data patterns, such as upside-down bathtub shapes.

Purpose of the Study:

  • To introduce and analyze a novel extension of the inverse Lindley distribution.
  • To assess the statistical properties and applicability of the proposed distribution for modeling lifetime data.

Main Methods:

  • Derivation of key statistical properties: density, hazard rate, moments, skewness, kurtosis, and quantile function.
  • Application of Maximum Likelihood Estimation (MLE) for parameter estimation.
  • Analysis of Rényi entropy for model uncertainty.
  • Comparative analysis with existing distributions using real-world flood level data.

Main Results:

  • The proposed extended inverse Lindley distribution demonstrates enhanced flexibility for upside-down bathtub data.
  • Statistical properties and estimation methods (MLE) were successfully derived.
  • The model provided a competitive fit when applied to the Susquehanna river flood level dataset.

Conclusions:

  • The extended inverse Lindley distribution is a valuable addition to the statistical modeling toolkit.
  • The distribution offers a more flexible approach for analyzing complex lifetime data, particularly those exhibiting upside-down bathtub behavior.
  • The model's performance on real-world data validates its practical utility.