Bayesian Estimation of The Ex-Gaussian Distribution

Abstract

Fitting of the exponential modified Gaussian distribution to model reaction times and drawing conclusions from its estimated parameter values is one of the most popular method used in psychology. This paper aims to develop a Bayesian approach to estimate the parameters of the ex-Gaussian distribution. Since the chosen priors yield to posterior densities that are not of known form and that they are not always log-concave, we suggest to use the adaptive rejection Metropolis sampling method. Applications on simulated data and on real data are provided to compare this method to the standard maximum likelihood estimation method as well as the quantile maximum likelihood estimation. Results shows the effectiveness of the proposed Bayesian method by computing the root mean square error of the estimated parameters using the three methods.

Estimation of Some Epidemiological Parameters With the COVID-19 Data of Mayotte

“…In terms of forthcoming study, we are currently interested in theoretical developments in a context of a cross-mixture in order to improve the estimates considering negative serial interval and α-stables distributions with stochastic Expectation-Maximization algorithm and Bayesian methods, refer to Castillo-Barnes et al [38] and El Haj et al [39]. As concerned the regression methods, we are currently working on some other non-parametric forms, refer to Slaoui [40] and Bouzebda and Slaoui [41].…”