Accurate estimates of farm-level crop yield probability density functions (PDF's) are crucial for studying various crop insurance programs and production under risk and uncertainty. Unfortunately, farm-level crop yield PDF's are difficult to estimate due to the lack of sufficient farm yield data. County yield data cover much longer time periods than farm yield data, but using county yield distributions to conjecture about farm yield distributions is dangerous. The theoretical reason is that county yield is the average of correlated farm yields, for which there is no recognizable probability density function (PDF). This paper investigates the relationship between farm and county yield distributions using both statistical theory and the Monte-Carlo simulation method. Results show that under suitable farm yield correlation and density structures, the shape of yield distribution at the farm level is similar to that at the county level. A method is then developed for estimating and simulating farm yield distributions based on county yield PDF estimates and information contained in farm yield data. Six candidate yield models: normal, beta, Weibull, inverse hyperbolic sine transformation, a mixture of normals, and kernel density estimators are applied to Branch County corn yields after detrending nonstationary yield data. Goodness-of-fit results for normal, beta and Weibull distributions show that Weibull best fits county yields. The method for simulating farm yields is illustrated using kernel density estimates.
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