A more flexible Lomax distribution: Characterization, estimation, group acceptance sampling plan and applications

Abstract

The objectives of this paper are threefold. First, we introduce a novel distribution, named the Odd Perks-Lomax (OPL) distribution, which is derived from the Odd Perks-G family of distributions. Second, we explore the mathematical properties of the OPL distribution in detail. Third, we develop a group acceptance sampling plan tailored for truncated life tests, utilizing this new distribution. The OPL distribution extends the classical Lomax distribution by incorporating two additional parameters, enhancing its flexibility. Hypothetical plots of the hazard and probability density functions suggest that the OPL distribution is versatile and capable of fitting a wide range of data. Parameters were estimated using the maximum likelihood method. Group acceptance sampling plans (GASPs) based on truncated life tests were designed, and their effectiveness was evaluated through simulation studies and real-world applications. Empirical data from both engineering and medical domains were analyzed, demonstrating that the OPL distribution outperforms traditional distributions, such as the Weibull and Exponentiated Weibull distributions. The maximum likelihood estimates obtained from these datasets were reintroduced into the GASP framework, further validating its utility in statistical quality control applications.

Keywords

• Odd Perks Lomax distribution
• Group acceptance sampling plan
• Maximum likelihood estimation
• Quantile function
• Quality
• Producer’s risk