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This is an accepted version of this page This is the latest accepted revision, reviewed on 17 December 2024. Observation that in many real-life datasets, the leading digit is likely to be small For the unrelated adage, see Benford's law of controversy. The distribution of first digits, according to Benford's law. Each bar represents a digit, and the height of the bar is the percentage of ...
English: illustration of Benford's law, using the population of the countries of the world. The chart depicts the percentage of countries having the corresponding digit as first digit of their population (red bars). For example, 64 countries of 237 (=27%) have 1 as leading digit of the population.
Law of truly large numbers; Central limit theorem; Regression toward the mean; Examples of "laws" with a weaker foundation include: Safety in numbers; Benford's law; Examples of "laws" which are more general observations than having a theoretical background: Rank–size distribution; Examples of supposed "laws" which are incorrect include: Law ...
In probability theory and statistics, the zeta distribution is a discrete probability distribution. If X is a zeta-distributed random variable with parameter s , then the probability that X takes the positive integer value k is given by the probability mass function
Benford's law : In many collections of data, a given data point has roughly a 30% chance of starting with the digit 1. Benford's law of controversy: Passion is inversely proportional to the amount of real information available. Bennett's laws are principles in quantum information theory. Named for Charles H. Bennett.
Benford's law, which describes the frequency of the first digit of many naturally occurring data. The ideal and robust soliton distributions. Zipf's law or the Zipf distribution. A discrete power-law distribution, the most famous example of which is the description of the frequency of words in the English language.
(Hasty generalization is the mistaken application of this law to small data sets.) Law of anomalous numbers (also called first-digit law and (Newcomb–)Benford law), an observation about the frequency distribution of leading digits in many real-life sets of numerical data. Pigeonhole principle, the occurrence of mathematical coincidences
The first two 'explanations' are patently absurd. The second shows that Benford's law is a limiting form of the zeta distribution but doesn't say why it works. The first never gives Benford's law. More precisely, as you count, the proportion of 1s increases, then the proportion of 2s until it equals the 1s, then the proportion of 3s, and so on.