Murphy E A
Am J Med Genet. 1979;4(2):173-90. doi: 10.1002/ajmg.1320040210.
A discussion of the primordial confusion between the multiplicative Galtonian ("lognormal") trait and the imperfectly segregating Mendelian trait is laid out from a probabilistic standpoint. Several criteria used in comparing them (bimodality; bitangentiality; goodness of fit to the multinomialized form of the distribution; cumulants of the distributions) are reviewed and the inadequacy of their probabilistic properties discussed in some detail. The logical asymmetry of the normalized score ("Roberts" correction") and hence its invalidity as a criterion for distinguishing between the models is pointed out. The form of a mixture of two Gaussian distributions with fixed and equal variances but with differing age-dependent means ("the Platt model") is explored. The epistemological implications are exhibited. As a first step to restoring symmetry, a general model is proposed of which these and other models in wide use emerge as special cases. No attempt is made to deal here with the statistical aspects of the problem.
从概率角度对乘法高尔顿（“对数正态”）性状与不完全分离的孟德尔性状之间的原始混淆进行了讨论。回顾了用于比较它们的几个标准（双峰性；双切性；对分布的多项式形式的拟合优度；分布的累积量），并详细讨论了它们概率特性的不足之处。指出了标准化分数（“罗伯茨”校正）的逻辑不对称性，因此其作为区分模型的标准是无效的。探讨了具有固定且相等方差但具有不同年龄相关均值的两个高斯分布的混合形式（“普拉特模型”）。展示了其认识论含义。作为恢复对称性的第一步，提出了一个通用模型，广泛使用的这些模型和其他模型都是该通用模型的特殊情况。这里不尝试处理该问题的统计方面。
