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Acceptance sampling plans for the three-parameter inverted Topp-Leone model.

Said G Nassr1,2, Amal S Hassan3, Rehab Alsultan4

  • 1Department of Statistics and Insurance, Faculty of Commerce, Arish University, Egypt.

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|January 19, 2023
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Summary
This summary is machine-generated.

A new transmuted power inverted Topp-Leone (TPITL) distribution is introduced, offering a flexible model for reliability and survival analysis. Maximum likelihood estimation generally performed best for this novel distribution.

Keywords:
maximum product spacingpower inverted Topp–Leone distributionstochastic orderingtransmuted family

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Area of Science:

  • Statistics
  • Probability Distributions
  • Reliability Engineering

Background:

  • The inverted Topp-Leone distribution is a key model in reliability and survival analysis.
  • Extensions of existing distributions are crucial for enhancing statistical modeling capabilities.
  • The quadratic rank transmutation map provides a method for generating new probability distributions.

Purpose of the Study:

  • To introduce a novel statistical distribution, the transmuted power inverted Topp-Leone (TPITL) distribution.
  • To explore the theoretical properties of the TPITL distribution, including its quantile function, moments, and uncertainty measures.
  • To develop and evaluate acceptance sampling plans for the TPITL distribution and assess various estimation techniques.

Main Methods:

  • The quadratic rank transmutation map was employed to derive the TPITL distribution.
  • Theoretical properties such as quantile function, moments, and uncertainty measures were derived.
  • Acceptance sampling plans were designed based on the median lifetime.
  • Five estimation methods (Maximum Likelihood, Least Squares, Weighted Least Squares, Maximum Product of Spacing, Cramer-von Mises) were applied.
  • Monte Carlo simulations were conducted to evaluate estimator performance.
  • The TPITL model was applied to real-world datasets for validation.

Main Results:

  • The TPITL distribution was successfully derived and its key properties were analyzed.
  • Maximum likelihood estimates generally exhibited the smallest mean squared errors.
  • Cramer-von Mises estimates showed superior performance in certain scenarios.
  • All estimation techniques demonstrated consistency as sample size increased.
  • The TPITL distribution proved to be a valid and adaptable model when compared to existing distributions on real data.

Conclusions:

  • The proposed TPITL distribution offers a valuable extension for reliability and survival data analysis.
  • Maximum likelihood estimation is a robust method for parameter estimation of the TPITL distribution.
  • The TPITL distribution demonstrates flexibility and good performance in modeling real-world data compared to other established distributions.