A numerical maximum likelihood (ML) estimation procedure is developed for the constrained parameters of multinomial distributions. The main difficulty involved in computing the likelihood function is the precise and fast determination of the multinomial coefficients. For this the coefficients are rewritten into a telescopic product. The presented method is applied to the ML estimation of the Zi...

We investigate the average sizes of the n largest fragments in nuclear multifragmentation events near the critical point of the nuclear matter phase diagram. We perform analytic calculations employing Poisson statistics as well as Monte Carlo simulations of the percolation type. We find that previous claims of manifestations of Zipf’s Law in the rank-ordered fragment size distributions are not ...

From the works of mathematical properties of songs, we construct the phylomemetic trees of Indonesian ethnic and traditional songs. The memeplexes are then reflected by the used notes and respective durations as they exhibit the Zipf-Mandelbrot law, the gyration coefficient, “spiraling effects”, and the dynamic entropy shown in the structure of the songs. The cladistic techniques yielding phylo...

Many recent caching systems aim to improve hit ratios, but there is no good sense among practitioners of how much further hit ratios can be improved. In other words, should the systems community continue working on this problem? Currently, there is no principled answer to this question. Most prior work assumes that objects have the same size, but in practice object sizes often vary by several o...

We observed that the coefficients of two important empirical statistical laws of language – Zipf law and Heaps law – are different for different languages, as we illustrate on English and Russian examples. This may have both theoretical and practical implications. On the one hand, the reasons for this may shed light on the nature of language. On the other hand, these two laws are important in, ...

We use the formulation of equilibrium statistical mechanics in order to study some important characteristics of language. Using a simple expression for the Hamiltonian of a language system, which is directly implied by the Zipf law, we are able to explain several characteristic features of human language that seem completely unrelated, such as the universality of the Zipf exponent, the vocabula...

The upper tail of the firm size distribution is often assumed to follow a Power Law behavior. Recently, using different estimators and on different data sets, several papers conclude that this distribution follows the Zipf Law, that is that the fraction of firms whose size is above a given value is inversely proportional to the value itself. We compare the different methods through which this c...

The paper revisits the investment simulation based on strategies exhibited by Generalized (m, 2)-Zipf law to present an interesting characterization of the wildness in financial time series. The investigations of dominant strategies on each specific time series shows that longer words dominant in larger time scale exhibit shorter dominant ones in smaller time scale and vice versa. Moreover, den...