Maximum likelihood estimation of the parameters of the inverse Gaussian distribution using maximum rank set sampling with unequal samples

2021 ◽  
pp. 1-21
Author(s):  
Shuo Wang ◽  
Wangxue Chen ◽  
Meng Chen ◽  
Yawen Zhou
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Gaussian Distribution ◽  
Likelihood Estimation ◽  
Inverse Gaussian Distribution ◽  
Inverse Gaussian ◽  
Maximum Rank ◽  
Rank Set Sampling

scholarly journals Bayesian Estimation of The Ex-Gaussian Distribution

2021 ◽  
Vol 9 (4) ◽  
pp. 809-819
Author(s):  
Abir El Haj ◽  
Yousri Slaoui ◽  
Clara Solier ◽  
Cyril Perret
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Gaussian Distribution ◽  
Estimation Method ◽  
Reaction Times ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimated Parameters ◽  
Parameter Values

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.

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