Estimate the Scale Parameter for Inverse Rayleigh Distribution via Maximum Likelihood with Trapezoidal Fuzzy Data
Keywords:
Centroid defuzzification methods, Trapezoidal fuzzy data, Inverse Rayleigh distribution, Maximum likelihood estimation, Monte Carlo simulationAbstract
In this work, the scale parameter of the inverse Rayleigh distribution (IRD) is estimated, which is one of the most important distributions in analyzing failure times and has broad applications in different fields. The data of this distribution are presumed to be trapezoidal fuzzy, and they were switched into classical data using two paths based on approaches, C and , introduced as novel fuzzy output conversion techniques. Three fuzziness classes were adopted: absolute fuzziness, asymmetric (severe) fuzziness, and symmetric (moderate) fuzziness, to assess the robustness of the estimators under varying degrees of imprecision. The estimation workflow was performed using maximum likelihood estimation (MLE), with simulation used to generate the data. The comparison between results depends on the mean squared error (MSE). All mathematical procedures were applied in MATLAB R2024b, and the results showed that the method outperformed in terms of estimation accuracy and lower error values. Indeterminate environments demand improved estimation accuracy when incorporating reliability models and defuzzification methods. This is evident through the practical importance referenced in these findings.
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