Estimation Methods of the Parameters in Fuzzy Pareto Distribution

Abstract

In this paper considered the estimation of the parameters in the Fuzzy Pareto Distribution of two parameters. Now we used the Method of moments, Method of Maximum likelihood, and Method of least squares. From this it seemed to establish the consistent parameters when the sample size is increased. This paper aims at sample size increased when the parameters are consistent.

Introduction

Table 1-3 gives the estimates of the parameters of the fuzzy pareto distribution by using different methods under different sample size with α-cut value is 0.2, 0.5 and 0.8 respectively. The (1,1), (1,2) and (3,2) also the estimates of shape and scale parameters in fuzzy pareto distribution were preferred Maximum Likelihood Estimation Method based on the least Means Square Error  and the seconded by Least Square Method and the Last by Method of Moment. But in alpha-cut manner the left alpha cut preferred in order as MLE, LSE and MME and in right alpha cut preferred in order as MME, LSE and MLE. The Table also shows that as the sample size increases, the parameter estimates tend to be closer to the original values. So far, estimation methods have demonstrated the properties of consistency.

By using the goodness of fit criteria of MSE and TD we prefered MLE method is the best method and followed by LSE and MME respectively by taking least and smaller values. (by Quandts 1964).

Conclusion

From the above results we conclude that the Maximum Likelihood Estimation method is more preferrable and suitable method for fitting the two parameter fuzzy pareto distribution. And also we proven that MLE is the most efficient estimator compared with Least Square Method and Method of Moment estimators. It is also conclude that analysis all the methods is the consistent. The alpha cut we used here to calculate the estimate parameters among from the imprecise data adequately.

References

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Copyright

Copyright © 2023 Pullooru Bhavana, Dr. D Kalpana Priya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.