Comparison of Various Ranking Methods with Pareto Distribution Methods in Imprecise Data

Abstract

The Pareto distribution has seen wide application in many different fields recently. Nowadays, the data we collect may be imprecise and contain uncertainties. This means that the values we gather cannot necessarily be considered a single, definitive value. In this paper, it is explored how various estimation methods like the method of moments, maximum likelihood estimation, and least squares estimation are used to determine the parameters of a Pareto distribution when the data is fuzzy or uncertain in nature. When making decisions, ranking methods are often heavily relied upon. For this reason, the application of several different ranking techniques to triangular fuzzy numbers (TFNs) is considered. The ranking methods for TFNs are found to tend to produce estimated parameters that are quite similar or even identical. The estimating parameters of a Pareto distribution can be solved for when dealing with fuzziness by the use of ranking methods such as alpha-cut, Yeager’s method, sub-interval method, Pascal method, magnitude method, and centroid method on the TFNs. By comparing the results of these various ranking techniques, an analysis is conducted to whether the estimated parameters of the Pareto distribution are consistent across the different ranking methods for TFNs get the uniqueness of the solution or differ. The decision making done by among the various ranking techniques, which method preferable for future comparison with extended of new ranking techniques. The conclusion is that the simulation results match up well with actual application data, serving as a good example for explaining this overall strategy.