A Simulation Study of Impacts of Estimated Method and Uncertainty on Parameters in Length-Weight Relationship

Abstract

To acknowledge the impacts of estimated method and uncertainty introduced into the weight on parameters in length - weight relationship, take the morphometric traits of Fenneropenaeus chinensis as example, the parameters a and b were estimated by using power of the absolute residuals (m, 1 ≤m (natural number) ≤ 20) methods, and error in the form of exponent was introduced into length – weight relationship. The study showed that the values of parameters in the relationship between length and weight were related to estimation methods. With the exponential increase of absolute residual, parameter a increased, while parameter b was highly uncertain. For the stability of parameter estimates, it was better to use the least absolute deviation method than the least square method and higher exponent of absolute residua to estimate the parameters. Uncertainty introduced into weight did not greatly impact the mean and median of the parameters a and b in the relationship between body length and weight. However, with increasing uncertainty, the fluctuation of parameter estimation increased, while the stability of the fitting effect of the length - weight relationship decreased. So, the estimated method and uncertainty should be taken into account for estimating the parameters in length - weight relationship, and the least absolute deviation method was proposed to estimate the parameters in length - weight relationship.