In this paper, we investigated the estimation and prediction problems based on current record statistics arising from the Weibull distribution. The Weibull model is widely used in industrial reliability, survival analysis, and environmental sciences. Under the assumption that the data represent current records from a two-parameter Weibull distribution with shape parameter $ k $ and scale parameter $ \lambda $, we derived the new probability density function (PDF) and cumulative distribution function (CDF) of upper and lower current records. After that, a closed-form expression for the moments of upper and lower current records was obtained. Later, the maximum likelihood and Bayesian estimators for the parameters were obtained, along with predictions of future current record values and a predictive interval. Monte Carlo simulation was performed to assess the performance of the proposed estimators under various sample sizes and parameter settings. The methodology was further illustrated using an application to industrial data from Saudi Arabia, demonstrating the practical relevance of Weibull record modeling for reliability and life-testing analysis.
Citation: Ramy Abdelhamid Aldallal. Bayesian estimation and prediction of Weibull current records with application to Saudi industrial data[J]. AIMS Mathematics, 2026, 11(2): 4369-4394. doi: 10.3934/math.2026175
In this paper, we investigated the estimation and prediction problems based on current record statistics arising from the Weibull distribution. The Weibull model is widely used in industrial reliability, survival analysis, and environmental sciences. Under the assumption that the data represent current records from a two-parameter Weibull distribution with shape parameter $ k $ and scale parameter $ \lambda $, we derived the new probability density function (PDF) and cumulative distribution function (CDF) of upper and lower current records. After that, a closed-form expression for the moments of upper and lower current records was obtained. Later, the maximum likelihood and Bayesian estimators for the parameters were obtained, along with predictions of future current record values and a predictive interval. Monte Carlo simulation was performed to assess the performance of the proposed estimators under various sample sizes and parameter settings. The methodology was further illustrated using an application to industrial data from Saudi Arabia, demonstrating the practical relevance of Weibull record modeling for reliability and life-testing analysis.
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Ramy Abdelhamid Aldallal. Bayesian estimation and prediction of Weibull current records with application to Saudi industrial data[J]. AIMS Mathematics, 2026, 11(2): 4369-4394. doi: 10.3934/math.2026175
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