Probability Distributions of Field Crop Yields

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Abstract
After first establishing an “a priori” expectation of nonnormality, the paper presents statistical analyses of several experimental series of field crop yields. This clinical examination suggests the following plausible inferences: The several series may be regarded as more or less random samples from stable parent probability distributions. Both normality and lognormality appear to be exceptions rather than the rule with respect to those distributions that may properly be inferred from the stochastic properties of the several series. The Pearson system of probability density functions is then applied to the data. The sample moments imply the type I (generalized Beta) skewed function of limited range as the general case. Estimates of this function are obtained for each series. The degree of skewness and kurtosis is shown to depend on nitrogen level. Implications for farm planning are discussed. Each statistical technique used is described and critically reviewed.

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