scholarly journals Power Laws, Prices and National Accounts: Are There Any Irregularities?

2020 ◽  
Author(s):  
Ciprian Florin Pater ◽  
Deni Mazrekaj
Keyword(s):  
Data Quality ◽  
Price Index ◽  
Consumer Price Index ◽  
Power Laws ◽  
Zipf’S Law ◽  
Benford’S Law ◽  
National Accounts ◽  
Zipf's Law ◽  
High Data ◽  
Benford's Law

Many economic regularities have been found to adhere to power laws. In this paper, we apply Benford’s law to consumer price index data from Norway and Zipf’s law on a Norwegian report about the history of Norwegian national accounts. Norway is a particularly interesting country to study as it scores among the highest-ranked countries on data quality. We find that the consumer price index adheres to Benford’s law, showing high data quality. On the other hand, our results do indicate that the report does not adhere to Zipf’s law.

scholarly journals On the authenticity of COVID-19 case figures

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0243123
Author(s):  
Adrian Patrick Kennedy ◽  
Sheung Chi Phillip Yam
Keyword(s):  
Empirical Evidence ◽  
Fraud Detection ◽  
Zipf’S Law ◽  
World Health ◽  
Benford’S Law ◽  
Surveillance Systems ◽  
Zipf's Law ◽  
Benford's Law ◽  
Formal Statistical Analysis ◽  
Health Organization

In this article, we study the applicability of Benford’s law and Zipf’s law to national COVID-19 case figures with the aim of establishing guidelines upon which methods of fraud detection in epidemiology, based on formal statistical analysis, can be developed. Moreover, these approaches may also be used in evaluating the performance of public health surveillance systems. We provide theoretical arguments for why the empirical laws should hold in the early stages of an epidemic, along with preliminary empirical evidence in support of these claims. Based on data published by the World Health Organization and various national governments, we find empirical evidence that suggests that both Benford’s law and Zipf’s law largely hold across countries, and deviations can be readily explained. To the best of our knowledge, this paper is among the first to present a practical application of Zipf’s law to fraud detection.

Benford's law, Zipf's law and the pore properties in solids

2020 ◽  
Vol 292 ◽  
pp. 109735
Author(s):  
Antigoni G. Margellou ◽  
Philippos J. Pomonis
Keyword(s):  
Zipf’S Law ◽  
Benford’S Law ◽  
Zipf's Law ◽  
Benford's Law ◽  
Pore Properties

scholarly journals Zipf's Law, Hierarchical Structure, and Cards-Shuffling Model for Urban Development

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Yanguang Chen
Keyword(s):  
Complex Systems ◽  
Hierarchical Structure ◽  
Spatial Dynamics ◽  
Social Institutions ◽  
Power Laws ◽  
Natural World ◽  
Zipf’S Law ◽  
Zipf's Law ◽  
Cascade Structure ◽  
The Individual

Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world and social institutions. Where there is a hierarchy with cascade structure, there is a Zipf's rank-size distribution, andvice versa. However, we have no theory to explain the spatial dynamics associated with Zipf's law of cities. In this paper, a new angle of view is proposed to find the simple rules dominating complex systems and regular patterns behind random distribution of cities. The hierarchical structure can be described with a set of exponential functions that are identical in form to Horton-Strahler's laws on rivers and Gutenberg-Richter's laws on earthquake energy. From the exponential models, we can derive four power laws including Zipf's law indicative of fractals and scaling symmetry. A card-shuffling model is built to interpret the relation between Zipf's law and hierarchy of cities. This model can be expanded to illuminate the general empirical power-law distributions across the individual physical and social sciences, which are hard to be comprehended within the specific scientific domains. This research is useful for us to understand how complex systems such as networks of cities are self-organized.

Benford’s Law and Macroeconomic Data Quality

2009 ◽  
Vol 09 (10) ◽  
pp. 1 ◽  
Author(s):  
Jesus Gonzalez-Garcia ◽  
Gonzalo C. Pastor ◽  
◽  
Keyword(s):  
Data Quality ◽  
Benford’S Law ◽  
Benford's Law

The logarithmic Zipf law in a general urn problem

2020 ◽  
Vol 24 ◽  
pp. 275-293
Author(s):  
Aristides V. Doumas ◽  
Vassilis G. Papanicolaou
Keyword(s):  
Social Sciences ◽  
Power Law ◽  
Random Variable ◽  
Power Laws ◽  
Zipf’S Law ◽  
Zipf's Law ◽  
The Social ◽  
Leading Term ◽  
Zipf Law ◽  
Highly Cited

The origin of power-law behavior (also known variously as Zipf’s law) has been a topic of debate in the scientific community for more than a century. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. In a highly cited article, Mark Newman [Contemp. Phys. 46 (2005) 323–351] reviewed some of the empirical evidence for the existence of power-law forms, however underscored that even though many distributions do not follow a power law, quite often many of the quantities that scientists measure are close to a Zipf law, and hence are of importance. In this paper we engage a variant of Zipf’s law with a general urn problem. A collector wishes to collect m complete sets of N distinct coupons. The draws from the population are considered to be independent and identically distributed with replacement, and the probability that a type-j coupon is drawn is denoted by pj, j = 1, 2, …, N. Let Tm(N) the number of trials needed for this problem. We present the asymptotics for the expectation (five terms plus an error), the second rising moment (six terms plus an error), and the variance of Tm(N) (leading term) as N →∞, when pj = aj / ∑j=2N+1aj, where aj = (ln j)−p, p > 0. Moreover, we prove that Tm(N) (appropriately normalized) converges in distribution to a Gumbel random variable. These “log-Zipf” classes of coupon probabilities are not covered by the existing literature and the present paper comes to fill this gap. In the spirit of a recent paper of ours [ESAIM: PS 20 (2016) 367–399] we enlarge the classes for which the Dixie cup problem is solved w.r.t. its moments, variance, distribution.

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