A novel extended inverse Weibull distribution: Statistical analysis and application

This paper proposes a new type of exponential-type Weibull distribution based on the inverse Weibull distribution --- the transformed inverse Weibull distribution. This distribution constructs a more flexible parameter structure through mathematical transformation and has a better fitting effect on actual data. We deeply analyzed the key statistical properties of this distribution, including the probability density function, survival function, quantile function, as well as Shannon entropy, Rényi entropy, Tsallis entropy, and Mathai-Haubold entropy, etc. In terms of parameter estimation, various parameter estimation methods such as maximum likelihood estimation and Bayesian estimation were adopted to estimate the parameters of the transformed inverse Weibull distribution, and the performance of various parameter estimation methods was evaluated through Monte Carlo simulation. Finally, two sets of real data were applied to verify the applicability and effectiveness of the model in practical applications. The results show that the transformed inverse Weibull distribution exhibits a superior fitting performance in the goodness-of-fit test compared to the Weibull distribution, weighted exponential distribution, exponential Pareto distribution, flexible Weibull distribution, generalized exponential distribution, and generalized inverse exponential distribution.