相关论文: Citations to articles citing Benford's law: a Benf…
A random variable X that is base b Benford will not in general be base c Benford when c is not equal to b. This paper builds on two of my earlier papers and is an attempt to cast some light on the issue of base dependence. Following some…
The exponential growth in the number of scientific papers makes it increasingly difficult for researchers to keep track of all the publications relevant to their work. Consequently, the attention that can be devoted to individual papers,…
The importance of statistical patterns of language has been debated over decades. Although Zipf's law is perhaps the most popular case, recently, Menzerath's law has begun to be involved. Menzerath's law manifests in language, music and…
Zipf's law in its basic incarnation is an empirical probability distribution governing the frequency of usage of words in a language. As Terence Tao recently remarked, it still lacks a convincing and satisfactory mathematical explanation.…
Business research is facing the challenge of scattered knowledge, particularly in the realm of brand loyalty (BL). Although literature reviews on BL exist, they predominantly concentrate on the pre-sent state, neglecting future trends.…
In this paper we show that the dramatic increase in the number of research articles indexed in the Web of Science database impacts the commonly observed distributions of citations within these articles. First, we document that the growing…
Half-life number sequences collected from nuclear data charts are found to obey the Newcomb-Benford law. Based on this fact, it has been suggested recently, that this law should be used to test the quality of nuclear decay models. In this…
We provide conditions on dependent and on non-stationary random variables $X_n$ ensuring that the mantissa of the sequence of products $\left(\prod_{1}^{n}X_k\right)$ is almost surely distributed following the Benford's law or converges in…
A plethora of natural and socio-economic phenomena share a striking statistical regularity, that is the magnitude of elements decreases with a power law as a function of their position in a ranking of magnitude. Such regularity is known as…
The textual, big-data literature misses Bentley, OBrien, & Brocks (Bentley et als) message on distributions; it largely examines the first-order effects of how a single, signature distribution can predict population behaviour, neglecting…
According to a popular belief, the decimal digits of mathematical constants such as {\pi} behave like statistically independent random variables, each taking the values 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 with equal probability of 1/10. If…
Among econophysics investigations, studies of religious groups have been of interest. On one hand, the present paper concerns the Antoinist community financial reports, - a community which appeared at the end of the 19-th century in…
In this paper we will look at the distribution with which passwords are chosen. Zipf's Law is commonly observed in lists of chosen words. Using password lists from four different on-line sources, we will investigate if Zipf's law is a good…
Journal Impact Factors (IFs) can be considered historically as the first attempt to normalize citation distributions by using averages over two years. However, it has been recognized that citation distributions vary among fields of science…
A hypothesis that the financial log-periodicity, cascading self-similarity through various time scales, carries signatures of a law is pursued. It is shown that the most significant historical financial events can be classified amazingly…
We investigate Sleeping Beauties (SBs) in medical research with a special focus on SBs cited in patents. We find that the increasing trend of the relative number of SBs comes to an end around 1998. However, still a constant fraction of…
Zipf's law for cities is probably the most famous regularity in social sciences. So much that, a hundred years of publication later, its status is not clear: is it a law of social organisation? Is it an instrument of description of city…
A Sleeping Beauty (SB) in science refers to a paper whose importance is not recognized for several years after publication. Its citation history exhibits a long hibernation period followed by a sudden spike of popularity. Previous studies…
The \textit{ternary digits of $2^n$} are a finite sequence of 0s, 1s, and 2s. It is a natural question to ask whether the frequency of any string of 0s, 1s, and 2s in this sequence approaches the same limit for all strings of the same…
The value of a social network is generally determined by its size and the connectivity of its nodes. But since some of the nodes may be fake ones and others that are dormant, the question of validating the node counts by statistical tests…