Bortkiewicz's Law

BORTKIEWICZ'S LAW, otherwise known as the "law of small numbers," consists in the fact that certain phenomena exhibit a high degree of correspondence between actual, observed fluctuations expressed in statistical numbers and theoretical fluctuations calculated in accordance with the law of normal errors ("stability" in the sense of Lexis), not in large, but in small masses. This "stability" is inherent in phenomena with a small number of occurrences, manifesting at large intervals of space and time or, expressed in terms of probability theory, phenomena with a small number of chances for the occurrence of each individual event. Logically, this proposition is explained by the fact that such rare phenomena, interspersed among masses of frequently occurring phenomena (e.g., suicide as one of the causes of death), retain the "stability" inherent in those masses, which yield large numbers. The "law of small numbers" is also historically connected with the latter, since it was noticed by Bortkiewicz as a result of studying the question of the "stability" of large numbers (see Lexis).