This study investigated the performance of the three estimators of surplus production model including process-observation-error-estimator with normal distribution (POE_N), observation-error-estimator with normal distribution (OE_N), and process-error-estimator with normal distribution (PE_N). The estimators with fat-tailed distributions including Student's t distribution and Cauchy distribution were also proposed and their performances were compared with the estimators with normal distribution. This study used Bayesian method, revised Metropolis Hastings within Gibbs sampling algorithm (MHGS) that was previously used to solve POE_N (Millar and Meyer, 2000), developed the MHGS for the other estimators, and developed the methodologies which enabled all the estimators to deal with data containing multiple indices based on catch-per-unit-effort (CPUE). Simulation study was conducted based on parameter estimation from two example fisheries: the Atlantic weakfish (Cynoscion regalis) and the black sea bass (Centropristis striata) southern stock.

Our results indicated that POE_N is the estimator with best performance among all six estimators with regard to both accuracy and precision for most of the cases. POE_N is also the robust estimator to outliers, atypical values, and autocorrelated errors. OE_N is the second best estimator. PE_N is often imprecise. Estimators with fat-tailed distribution usually result in some estimates more biased than estimators with normal distribution. The performance of POE_N and OE_N can be improved by fitting multiple indices. Our study suggested that POE_N be used for population dynamic models in future stock assessment. Multiple indices from valid surveys should be incorporated into stock assessment models. OE_N can be considered when multiple indices are available.