Advances and Applications in Statistics
Volume 3, Issue 3, Pages 217 - 228
(December 2003)
|
|
A GENERALIZED BENFORD LAW AND ITS APPLICATION
Werner Hürlimann (Switzerland)
|
Abstract: A
simple one-parameter analytical extension of
Benford’s law for first digits of numerical
data is constructed. Based on the maximum
likelihood method, the fitting capabilities of
the new distribution is illustrated at some
interesting and important integer sequences
including the numeri ideoni, the Keith,
Princeton, Lucky, Ulam and Bell numbers, as
well as the sequence of primes. Benford’s
law of the mixing of the considered data sets
is rejected at the 5% significance level while
the generalized Benford law is accepted with a
25% p-value.
Confirming the statistical evidence, it is
shown that the first digits of the Bell
numbers satisfy Benford’s law. |
Keywords and phrases: first digit, Benford’s law, uniform distribution, triangular distribution, two-sided power distribution, integer sequences, mixing sequences, Bell number. |
|
Number of Downloads: 339 | Number of Views: 1251 |
|