Fuzzy Reliability, Bayesian Estimation and Goodness of Fit Test for A Novel One Parameter Model with Simulation Study and Application

Abstract

This study investigates the goodness-of-fit test, fuzzy reliability analysis, and Bayesian estimation for a novel one-parameter probability distribution. Specifically, we introduce and analyze the exponential-Lindley and exponential-X-Lindley distributions as extensions of the proposed model. Using comprehensive analytical techniques, several key statistical properties of the distribution are derived and thoroughly examined. To assess the model's behavior under uncertainty, fuzzy reliability measures are developed, demonstrating its robustness and practical applicability in scenarios involving imprecise or vague data. Furthermore, a variety of parameter estimation methods—including classical and Bayesian approaches—are explored to assess the flexibility and precision of the proposed model. A simulation study is conducted using randomly generated datasets to evaluate the performance of the estimation techniques and to gain deeper insights into the model’s adaptability across different conditions. Finally, the model’s adequacy is validated using a goodness-of-fit test, confirming its potential usefulness in reliability and lifetime data analysis.