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Estimating the Parameters of Normal Distribution from Imprecise Data

In the literature, conventional statistical analyses of normal distribution are provided by using precise. However, in real-world situations, the results of an experimental performance can not always be in the form of exact numbers, and the measurements may be described by means of fuzzy samples. In this article, assuming that the available data are reported by fuzzy values, we extend the classical procedures of the estimation for the two-parameter normal distribution. First, we use a Newton-Raphson method to determine maximum likelihood estimates of parameters. Then, an approximation based on the Laplace approximation is used to calculate the Bayes estimates of the unknown parameters. Also, to compute the moment estimates of the parameters, an iterative numerical procedure is proposed. Finally, simulation studies are conducted in order to evaluate the performances of the proposed estimators and an analysis of one real data set is provided.