VIII.—On the Theory of Graduation
VIII.—On the Theory of Graduation
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八、论毕业论
DOI：
10.1017/s0370164600020800
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发表时间：
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通讯作者：
Edmund Taylor Whittaker
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作者：
Edmund Taylor Whittaker
数学理论的毕业或调整，迄今已发展主要与精算科学的需要，中心围绕以下问题：一组数字u1，u2，u3，. u n应该已经获得从观察或统计的某种。这些数字将代表一个变量u x的值，对应于它的自变量x的值1，2，. n，如果它们不受由于观测误差或统计不完善而引起的偶然不规则性的影响。人们希望构造一组数字，这些数字表示与这些x值相对应的变量u x的最可能的真值，使得“分级”数字与“未分级”数字u 1，u 2，. u n的差异尽可能小，但不受偶然的不规则性的影响，从而形成“平滑”序列，即可以形成用于各种计算的规则差分表的序列。
The mathematical theory of graduation or adjustment , which hitherto has been developed chiefly in connection with the needs of actuarial science, centres round the following problem: A set of numbers u 1 , u 2 , u 3 , … u n is supposed to have been obtained from observations or statistics of some kind. These numbers would represent the values of a variable u x corresponding to the values 1, 2, … n of its argument x , were it not that they are affected by accidental irregularities due to errors of observation, or to the imperfections of statistics. It is desired to construct a set of numbers , which represent the most probable true values of the variable u x corresponding to these values of x , so that the “graduated” numbers differ as little as possible from the “ungraduated” numbers u 1 , u 2 , … u n , but are freed from the accidental irregularities, and thus form a “smooth” sequence, i.e. a sequence from which a regular difference-table can be formed for use in various calculations.