Inference drawn on Logistic Distribution in the Presence of Fuzzy Data: Classical and Bayesian Approach

This paper investigates parameter estimation for the logistic distribution in the presence of fuzzy data, which introduces uncertainty and imprecision into the analysis. To handle this, we employ both classical and Bayesian frameworks. As closed-form solutions for Maximum Likelihood Estimators (MLEs) are not available under fuzzy conditions, the Expectation-Maximization (EM) algorithm is utilized to obtain numerical estimates. Asymptotic confidence intervals are then constructed based on these estimates. For Bayesian inference, we consider a conjugate prior and apply Lindley’s approximation and Approximate Bayesian Computation (ABC) to derive Bayes estimators, addressing the analytical intractability of the posterior distributions. Furthermore, advanced Markov Chain Monte Carlo (MCMC) methods namely Hamiltonian Monte Carlo (HMC) and the Metropolis-Hastings (MH) algorithm are employed to sample from posterior distributions and to construct Highest Posterior Density (HPD) intervals. The performance of all proposed estimators is assessed through extensive simulation studies. Finally, the practical utility of the methodologies is illustrated using a real-world dateset.