Statistical inference and applications of a new transforming weibull distribution.

This paper aims to construct a new transformed Weibull distribution model by mathematically transforming the Weibull distribution model. This model significantly enhances its applicability and flexibility by adjusting the shape and scale parameters of the random variables. We have detailed the analysis of the key statistical properties of the transformed Weibull distribution, including survival function, hazard function, quantile function, moment and moment-generating function, and order statistics, and have explored its heavy-tailed characteristics through mathematical proofs. We employed maximum likelihood estimation to estimate the model parameters and constructed asymptotic confidence intervals for the parameters. In addition, considering the application of Bayesian estimation under both information prior and non-information prior conditions, we used mixed Gibbs sampling to estimate the parameters under the Q-symmetric entropy loss function and the DeGroot loss function, and determined Bayesian credible intervals. To evaluate the performance of the estimation methods, we used Monte Carlo simulation to obtain the average parameter estimates under various estimation methods, and measured the accuracy of the estimation using mean square errors and mean biases. The applicability and effectiveness of the transformed Weibull distribution in practical data analysis have been confirmed by applying it to two real datasets.