Use Maximum Likelihood Method to Estimate the Non-normal Complete Randomized Design .

In this paper, a complete randomized design (CRD) was used in case the number of replicates of the experiment was equal and only one observation was recorded and on the assumption that the experimental error term follows a non-normal distribution, and the importance of distributions with heavy tails is because they are a generalization for all Non-normal distributions: It was assumed that the error term follows the extension hyperbola distribution (ehd) and Laplace distribution(Ld), and based on the traditional method represented by the maximum likelihood method, the design parameters were estimated when the mathematical model was fixed once and random again. We concluded that the estimates of the model parameters when the experimental error follows a Laplace distribution (Ld) are similar to the estimates of the model parameters when the error is normal. Given the difficulty of obtaining an agricultural experiment that follows the (ehd) and (Ld), an experimental experiment was used through the MATLAB program, through the mean square error criterion, a comparison was made between the fixed and random mathematical model for a completely random design under different values of additional and torsion parameters. Through the experimental results, it was shown that the values of the mean square error criterion for the fixed and random mathematical model decreased as the additional parameters values decrease and for (ehd).