Fuzzy Estimators for Parameters and Hazard Rate Function of Lindley Distribution: Simulation Study

The quantitative description of data is very essential for statistics. In standard statistics data are assumed to be numbers, vectors or classical functions. But in applications, real data are frequently not precise numbers or vectors, but often more or less imprecise. All kinds of data which cannot be presented as precise numbers or cannot be precisely classified are called non-precise or fuzzy. The present paper focused on obtaining the maximum likelihood and approximate Bayesian estimators of the parameters and hazard rate function for Lindley distribution when the data are available in fuzzy form. Since there are no exact forms, maximum likelihood estimators have been derived according to the algorithm of Newton- Raphson as an iterative technique and Bayes estimators have been derived based on informative gamma priors relative to squared error and precautionary loss functions according to a numerical approximate Lindley's technique. The obtained estimators have been compared through Monte-Carlo simulation study.