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ESTIMATING THE PARAMETERS OF THE STATISTICAL UPPER BOUND OF DRY HEPATOPANCREAS WEIGHT OF YABBIES (CHERAX ALBIDUS) BY THE EM1 ALGORITHM
Yuk W. Cheng (Australia) and Craig S. Lawrence (Australia)

Abstract:
This study was motivated by the data on the relationship between the dry hepatopancreas weight and body weight of yabbies (Cherax albidus). The model consists of two sources of variability in the data. One is the vertical spread that describes the condition of yabbies. The other is the even intrinsic variability present in the yabbies with complete growth conditions in dry hepatopancreas weight. A statistical method is presented for estimating the parameters of a nonlinear regression curve that describes the upper bound of the relationship between dry hepatopancreas weight and body weight. The EM1 algorithm is applied for the purpose of maximizing the complete data log likelihood. Additionally, nonlinear regression is used to estimate the initial guessed solution in the EM1 algorithm. The BIC criterion is proposed to select the best model. The statistical inference of all parameters is obtained directly from the observed log likelihood by Newton-Raphson algorithm. From the results of nonlinear upper bound regression, the largest male and female yabbies with body weight 90.96 g and 78.36 g had the best growth condition. Thus, farmers can optimize farming strategies to harvest yabbies from ponds or dams to obtain animals in good growth condition with different sex before they pass through the optimum complete body weight.

Keywords and phrases: mixture distribution, Newton-Raphson algorithm, observed log likelihood, complete data log likelihood.

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