Unified representation of Zipf distributions

Comparação da Lei de Zipf em conteúdos textuais e discursos orais

“…A aplicação desta lei enuncia que existe uma lei do menor esforço (Egghe, 1991;Zörnig;Altmann, 1995;Günther et al, 1996), onde algumas palavras/terminologias representam consensos de um campo ou área/subárea, podendo ser considerado trivial as informações de maior relevância, interessante as informações intermediárias e de ruído as informações soltas e de pouca frequência (Quoniam et al, 1998).…”

Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics

“…The apparent convergence to roughly 200 decimals can be verified against the right-hand side of Eq. (48). Of course, the right-hand side of Eq.…”

“…The three distributions, Zipf (zeta), Zipf-Mandelbrot (generalized zeta), and Good (Jonquière), are special cases of the Lerch distribution, and their properties can be expressed in terms of Lerch's transcendent with special values of the parameters. (See [48] for the discussion of relations between these distributions and the zero-truncated Lerch distribution. )…”

“…(55)] into an integral plus correction terms. In order to calculate (48) to an accuracy of 200 decimals, Eq. (56) says that we would be required to add on the order of 10 205 terms.…”

New integrated view at partial-sums distributions

“…Ψ -Digamma function (see in [1], [23]) under the summation with f (x, j) = 1 1 + µ , µ is the mean of this parent distribution. The resulting distribution {Q j } j∈{0,1,...,n} has probability generating function 3 F 2 (−n, 1, 1; 2, 2; 1 − t) and probability mass function 1 n + 1 n i=x 1 i + 1 x∈{0,1,...,n} (see in [5]).…”