A DB estimation method for the E-MN probability distribution parameters with applications in humanities

One of the humanities' most basic topics is the response time to creative problem-solving and decision-making in this field. In recent years, response time modeling by fitting an exponentially-modified normal (E-MN) probability distribution and the results obtained from this process have been widely used. The E-MN probability distribution results from the convolution of a normal probability distribution and an exponential probability distribution and contains three parameters. In this paper, a developed Bayesian (DB) estimation method is introduced to estimate the parameters of an E-MN probability distribution. This new estimation method uses the adaptive rejection Metropolis-Hastings (ARM-H) sampling method. The reason for this is that in normal mode and based on the classical Bayesian estimation method, the chosen prior probability density functions (pdfs) lead to posterior pdfs with unknown form and, they are not always logarithmically concave. Also, respectively, simulation and real data sets study have been done to demonstrate the better performance of the DB estimation method than the two other well-known estimation methods used in this context, including the maximum likelihood (ML) estimation method and the quantile maximum likelihood (QML) estimation method. To show the better efficiency of the proposed estimation method compared with the two other estimation methods, the root mean squared error (RMSE) criterion is used.