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Group acceptance sampling plan based on truncated life tests for Type-I heavy-tailed Rayleigh distribution
Mmesoma P Nwankwo1, Najwan Alsadat2, Anoop Kumar3
1Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, P.O. Box 5025, Awka, Nigeria.
Heliyon
|October 10, 2024
Summary
The Type-I heavy-tailed Rayleigh (TI-HTR) distribution offers a robust statistical model for analyzing data, particularly effective for COVID-19 and Cancer datasets. This heavy-tailed distribution provides better model fitting and inference compared to traditional methods.
Area of Science:
- Statistics
- Probability Distributions
- Statistical Modeling
Background:
- The Type-I heavy-tailed (TI-HT) family of distributions is a notable area of statistical research.
- The Type-I heavy-tailed Rayleigh (TI-HTR) distribution is a specific member of this family, requiring detailed characterization.
Purpose of the Study:
- To thoroughly investigate the statistical properties of the TI-HTR distribution.
- To develop and evaluate parameter estimation techniques, including maximum likelihood and penalized likelihood estimation.
- To assess the utility of the TI-HTR distribution in real-world applications and compare it with existing models.
Main Methods:
- Derivation of key statistical properties: moments, quantile function, and reliability measures.
- Application of maximum likelihood estimation (MLE) and penalized likelihood estimation (PLE) for parameter estimation.
- Graphical analysis of distribution functions and analytical investigation of model behavior.
- Design and evaluation of a group acceptance sampling plan (GASP) based on the TI-HTR distribution.
- Modeling of real-life COVID-19 and Cancer data.
Main Results:
- The TI-HTR distribution exhibits linear growth near the origin and rapid exponential decay, with tail behavior distinct from traditional power-law heavy tails.
- The TI-HTR distribution provides a superior fit to COVID-19 and Cancer data compared to competing models, leading to improved inference.
- Penalized likelihood estimation demonstrated superior performance with minimal standard errors for parameter estimates.
- The Cramér-von Mises test indicated the TI-HTR distribution's suitability for fast-decaying exponential data, showing less sensitivity to heavy tails.
Conclusions:
- The TI-HTR distribution is a valuable statistical tool, particularly for modeling datasets with fast-decaying exponential characteristics, such as COVID-19 and Cancer data.
- Penalized likelihood estimation is recommended for parameter estimation due to its improved accuracy and reduced standard errors.
- The TI-HTR distribution offers advantages in terms of model fit and inferential capabilities over traditional models for specific data types.
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