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<p>In almost every field of science, the decision about the population is based on the sampled data, usually recorded in the form of precise numbers. Statistics provide solid methods and models to streamline the raw observations into useful information. Over the decades, lifetime observations have been recorded as precise numbers, and a significant number of models have been developed to cover the random uncertainty in the obtained lifetime observations in life and engineering sciences. But with advancements in technology, a large sample of lifetime observations became difficult; therefore, Bayesian approaches are used for small sample sizes. Furthermore, advanced metrology suggests that exact measurements of continuous phenomena are not possible, and measurements also have another kind of uncertainty called fuzziness. Therefore, for the best possible inference, it is essential to cover all possible uncertainties. For this reason, lifetimes should be measured and recorded using up-to-date fuzzy numbers. This study aims to develop the Bayesian parameter estimators for important lifetime models to cover both uncertainties, i.e., fuzziness and random variation. To integrate all the available information in the suggested estimators, generalized Bayesian estimators for lifetime distributions, i.e. exponential and gamma distributions, are proposed, using fuzzy informative and non-informative priors along with fuzzy lifetimes and fuzzy hyperparameters. The proposed estimators are considerably useful compared to the classical estimators because they address both uncertainties, <b>i.e. random variation and fuzziness</b> present in lifetime observations, whereas the classical estimators only cover one, <b>only random variation</b>. Furthermore, interesting results are obtained that show the parameters of posterior density have a much increased fuzziness as compared to the fuzziness in lifetimes and the fuzziness in hyperparameters. These results provide strong evidence that fuzziness in lifetime observations should not be ignored. Ignoring the fuzziness could result in misleading inference. Consequently, it is essential to consider and incorporate this fuzziness when making inferences or evaluating lifetime data.</p>

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Generalized Bayesian Estimation of Survival Time Distributions Using Informative and Non-informative Priors Based on Fuzzy Information

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Muhammad Shafiq,
  • Saqib Waheed,
  • Umair Khalil,
  • Tmader Alballa,
  • Hamiden Abd El-Wahed Khalifa

摘要

In almost every field of science, the decision about the population is based on the sampled data, usually recorded in the form of precise numbers. Statistics provide solid methods and models to streamline the raw observations into useful information. Over the decades, lifetime observations have been recorded as precise numbers, and a significant number of models have been developed to cover the random uncertainty in the obtained lifetime observations in life and engineering sciences. But with advancements in technology, a large sample of lifetime observations became difficult; therefore, Bayesian approaches are used for small sample sizes. Furthermore, advanced metrology suggests that exact measurements of continuous phenomena are not possible, and measurements also have another kind of uncertainty called fuzziness. Therefore, for the best possible inference, it is essential to cover all possible uncertainties. For this reason, lifetimes should be measured and recorded using up-to-date fuzzy numbers. This study aims to develop the Bayesian parameter estimators for important lifetime models to cover both uncertainties, i.e., fuzziness and random variation. To integrate all the available information in the suggested estimators, generalized Bayesian estimators for lifetime distributions, i.e. exponential and gamma distributions, are proposed, using fuzzy informative and non-informative priors along with fuzzy lifetimes and fuzzy hyperparameters. The proposed estimators are considerably useful compared to the classical estimators because they address both uncertainties, i.e. random variation and fuzziness present in lifetime observations, whereas the classical estimators only cover one, only random variation. Furthermore, interesting results are obtained that show the parameters of posterior density have a much increased fuzziness as compared to the fuzziness in lifetimes and the fuzziness in hyperparameters. These results provide strong evidence that fuzziness in lifetime observations should not be ignored. Ignoring the fuzziness could result in misleading inference. Consequently, it is essential to consider and incorporate this fuzziness when making inferences or evaluating lifetime data.