Fuzzy Parameter Modeling and Survival Function Estimation for Inverse Power Maxwell Data

Abstract

This paper investigates the problem of estimating the survival function for lifetimes modeled by the fuzzy inversepower Maxwell distribution, motivated by reliability and survival data subject to vagueness and imprecision in observationsand parameters. The classical inverse power Maxwell model is first reviewed and its main distributional properties relevant tosurvival analysis are derived, including the probability density function, cumulative distribution function, survival function,and hazard rate. To capture epistemic uncertainty inherent in practical lifetime studies, the model parameters are thenrepresented as fuzzy numbers, and the corresponding fuzzy survival function is constructed via the extension principle underappropriate α − cut formulations. Several estimation strategies for the fuzzy survival function are developed, includingplug-in estimation based on maximum likelihood estimators of the crisp parameters, fuzzy least-squares-type procedures,and a possibility-based approach; explicit computational forms and algorithmic steps are provided for each method. Acomprehensive Monte Carlo simulation study is conducted to compare the finite-sample behavior of the proposed estimatorsin terms of bias, mean squared error, and coverage characteristics across different degrees of fuzziness, sample sizes, andparameter configurations. The practical usefulness of the methodology is illustrated with a real data set from survival studies,where the inverse power Maxwell model with fuzzy parameters yields more flexible survival function estimates than itsclassical counterpart and better accounts for expert judgement and imprecise measurements. The results indicate that theproposed fuzzy inference framework provides a robust and informative tool for survival analysis when ambiguity in lifetimedata cannot be ignored.