1925/01/01 by E. T. Whittaker · 3 citations
Mathematics · #Benford’s Law and Fraud Detection
paper · doi:10.1017/s0370164600020800
openalex publication_date 1925/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
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.