A Novel Approach of Elicitation Procedure of The Generalized Trapezoidal Uniform Parameters by IVBM-Algorithm

الملخص

A simple elicitation procedure has been developed for the 6-parameter generalized trapezoidal uniform and trapezoidal distributions, assuming that the modal range needs to be estimated. Based on this procedure, a novel algorithm, called the Initial-Values-Bounded-Maximum (IVBM) algorithm, is proposed to estimate the unknown parameters of the 6-parameter generalized trapezoidal uniform and trapezoidal distributions. The algorithm is summarized in three steps, demonstrating how to estimate the parameters of distributions composed of three parts. It can also be applied to simpler distributions, such as triangular or uniform distributions. The significance of this work lies in introducing an efficient and flexible algorithm for parameter estimation in complex distributions, producing accurate and stable results that enhance the reliability of statistical and predictive modeling across various fields. A practical example is provided to illustrate the application of the IVBM algorithm to generalized trapezoidal uniform and trapezoidal distributions. The results indicate a consistent decrease in mean square error (MSE) as the number of iterations increases, highlighting the algorithm’s effectiveness. Additionally, its adaptability allows it to improve the accuracy of models in diverse applications, enhancing both its theoretical and practical value.