Introducing the Beta-Shifted Power Family: A New Generator for Modeling Reliability and Survival Time
DOI:
https://doi.org/10.31185/bsj.Vol21.Iss37.1438Keywords:
Beta-Shifted Power distribution; generator families; lifetime modeling; survival analysis; reliability models; maximum likelihood estimation; Monte-Carlo simulation; parameter instability Weibull baseline, Lomax distribution, Log-logistic model; flexible distributions.Abstract
In this work, we propose the Beta-Shifted Power (BSP) generator, a flexible three-parameter family constructed using a shifted-power transformation of an existing baseline model for the generation of new lifetime distributions. The BSP family is formulated theoretically, comprising the probability density function (PDF), cumulative distribution function (CDF), reliability measures, and significant structural properties. Maximum likelihood estimation (MLE) of model parameters is derived, and an investigation into small sample properties is conducted via Monte-Carlo simulation. A comprehensive simulation study was conducted using a Weibull baseline, demonstrating that the BSP generator provides stable and consistent parameter estimation as sample size increases. The model successfully resolves identifiability issues found in simpler baseline configurations. The paper concludes with proposed remedies and avenues for future research, such as different settings for the baseline sequence and improved estimation techniques. In summary, the findings highlight that new generator families should be carefully analyzed regarding identifiability conditions.
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