The Σ-∆ background estimation is a simple non linear method of background subtraction based on comparison and elementary increment/decrement. We propose here some elements of justification of this method with respect to statistical estimation, compared to other recursive methods: exponential smoothing, Gaussian estimation. We point out the relation between the Σ-∆ estimation and a probabilistic...

We study a resource utilization scenario characterized by intrinsic fitness. To describe the growth and organization of different cities, we consider a model for resource utilization where many restaurants compete, as in a game, to attract customers using an iterative learning process. Results for the case of restaurants with uniform fitness are reported. When fitness is uniformly distributed, ...

Variables in large data sets in biology or e-commerce often have a head, made up of very frequent values and a long tail of ever rarer values. Models such as the Zipf or Zipf–Mandelbrot provide a good description. The problem we address here is the visualization of two such long-tailed variables, as one might see in a bivariate Zipf context. We introduce a copula plot to display the joint behav...

the relation between the variants of the frequency and the length of the word is among the laws that george kinsley zipf discovered, according to which, the longer is the length of a word, the less is the frequency of its application in the text. it is tried in the present research to examine this law, which has not been so far examined on the arabic language of the qur’ān, with a concentration...

A diagnostic of a power law distribution is that a log-log plot of frequency against rank yields a (nearly) straight line. For instance, Zipf (1935) plotted word token counts in a variety of texts against the inverse rank of each distinct word type and showed that typically such plots approximate a straight line. The characteristic ‘Zipf curve’ of word frequency against rank deviates from this ...

The distribution N(x) of citations of scientific papers has recently been illustrated (on ISI and PRE data sets) and analyzed by Redner [Eur. Phys. J. B 4, 131 (1998)]. To fit the data, a stretched exponential (N(x) ∝ exp−(x/x0) ) has been used with only partial success. The success is not complete because the data exhibit, for large citation count x, a power law (roughly N(x) ∝ x for the ISI d...