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A new one-parameter lifetime distribution and its regression model with applications.

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A new one-parameter lifetime distribution, an extension of the half-logistic distribution, is proposed for improved statistical modeling. This novel distribution offers simpler mathematical forms and demonstrates superior performance compared to existing models in real-world data analysis.

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Area of Science:

  • Statistics
  • Probability Theory
  • Reliability Engineering

Background:

  • Lifetime distributions are crucial for analyzing data related to the duration of events or systems.
  • Existing sophisticated lifetime distributions often suffer from complex parameter estimation due to numerous parameters.
  • There is a need for simpler yet effective lifetime distributions for accurate data modeling.

Purpose of the Study:

  • To introduce a new, one-parameter extension of the half-logistic distribution using the odd Lindley-G family.
  • To investigate the mathematical properties and estimation methods for the proposed distribution.
  • To develop and analyze a new log-location-scale regression model based on this novel distribution.

Main Methods:

  • Mathematical derivation of statistical properties including moments, quantile function, and Rényi entropy.
  • Parameter estimation using Maximum Likelihood, Least Square, Weighted Least Square, and Cramer-von Mises methods.
  • Simulation studies for performance comparison under complete and Type-II censored samples.
  • Application to real-world data sets and residual analysis of the proposed regression model.

Main Results:

  • The proposed one-parameter distribution exhibits simple mathematical forms and tractable properties.
  • Simulation results indicate the performance of different estimation methods for the new distribution.
  • Empirical analysis on three real data sets shows the proposed distribution outperforms competitive models, including other half-logistic extensions.

Conclusions:

  • The novel one-parameter extension of the half-logistic distribution provides a valuable and simpler alternative for lifetime data analysis.
  • The proposed distribution and its associated regression model offer improved modeling capabilities.
  • The study highlights the effectiveness of the new distribution in practical applications.