Despite abundant literature on crop yield distributions, there is no strict agreement about functional form and distributional assumptions. This paper estimated the optimal nitrogen rates in wheat production assuming a stochastic plateau yield function with nonnormal random effects. The yield plateau parameter is assumed to be beta distributed. The parameters are estimated using a Bayesian estimation methods and a noninformative prior. The maximum likelihood method was also used to compare the results of the two approaches. The results indicate a slight difference in nitrogen recommendation, which can be associated with the fact that the Bayesian methods capture parameter uncertainty while the MLE does not.