On the Newcomb-Benford law in models of statistical data.

Título inglés	On the Newcomb-Benford law in models of statistical data.
Título español	La ley de Newcomb-Benford en modelos de datos estadísticos.
Autor/es	Hobza, Tomás ; Vajda, Igor
Organización	Dep. Mat. FJFI CVUT, Praga, Repúb. Checa;Inst. Inform. Theor. Autom. Acad. Sci. Czech Repub., Praga, Repúb. Checa
Revista	1139-1138
Publicación	2001, 14 (2): 407-420, 8 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	We consider positive real valued random data X with the decadic representation X = Σi=∞∞Di 10i and the first significant digit D = D(X) in {1,2,...,9} of X defined by the condition D = Di ≥ 1, Di+1 = Di+2 = ... = 0. The data X are said to satisfy the Newcomb-Benford law if P{D=d} = log10(d+1 / d) for all d in {1,2,...,9}. This law holds for example for the data with log10X uniformly distributed on an interval (m,n) where m and n are integers. We show that if log10X has a distribution function G(x/σ) on the real line where σ>0 and G(x) has an absolutely continuous density g(x) which is monotone on the intervals (-∞,0) and (0,∞) then |P{D=d} - log10(d+1 / d)| ≤ 2g(0) / σ. The constant 2 can be replaced by 1 if g(x) = 0 on one of the intervals (-∞,0), (0,∞). Further, the constant 2g(0) is to be replaced by ∫|g'(x)| dx if instead of the monotonicity we assume absolute integrability of the derivative g'(x).
Clasificación UNESCO	120903
Palabras clave español	Distribución asintótica ; Distribución logarítmica ; Análisis de datos
Código MathReviews	MR1871305
Código Z-Math	Zbl 1006.62010
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