POWER-LAW DISTRIBUTIONS BASED ON EXPONENTIAL DISTRIBUTIONS: LATENT   SCALING, SPURIOUS ZIPF&apos;S LAW, AND FRACTAL RABBITS

doi:10.1142/S0218348X15500097

CORC > 北京大学 > 城市与环境学院

	POWER-LAW DISTRIBUTIONS BASED ON EXPONENTIAL DISTRIBUTIONS: LATENT SCALING, SPURIOUS ZIPF'S LAW, AND FRACTAL RABBITS
	Chen, Yanguang
刊名	FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
	2015
关键词	Inverse Power Law Exponential Distribution Latent Scaling Clark&apos Zipf&apos Fractals Urban Form City-Size Distribution URBAN-POPULATION DENSITY RANK-SIZE RULE GROWTH PATTERNS CITIES MODELS SETTLEMENTS PERSPECTIVE DIMENSION SYSTEMS SHAPE s Law s Law
DOI	10.1142/S0218348X15500097
英文摘要	The difference between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law distribution with the exponential distribution has been seldom researched. This paper is devoted to exploring the relationships between exponential laws and power laws from the angle of view of urban geography. Using mathematical derivation and numerical experiments, I reveal that a power-law distribution can be created through a semi-moving average process of an exponential distribution. For the distributions defined in a one-dimension space (e.g. Zipf's law), the power exponent is 1; while for those defined in a two-dimension space (e.g. Clark's law), the power exponent is 2. The findings of this study are as follows. First, the exponential distributions suggest a hidden scaling, but the scaling exponents suggest a Euclidean dimension. Second, special power-law distributions can be derived from exponential distributions, but they differ from the typical power-law distributions. Third, it is the real power-law distributions that can be related with fractal dimension. This study discloses an inherent link between simplicity and complexity. In practice, maybe the result presented in this paper can be employed to distinguish the real power laws from spurious power laws (e.g. the fake Zipf distribution).; SCI(E); EI; ARTICLE; chenyg@pku.edu.cn; 2; 23
语种	中文
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/419736]
专题	城市与环境学院
推荐引用方式 GB/T 7714	Chen, Yanguang. POWER-LAW DISTRIBUTIONS BASED ON EXPONENTIAL DISTRIBUTIONS: LATENT SCALING, SPURIOUS ZIPF'S LAW, AND FRACTAL RABBITS[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY,2015.
APA	Chen, Yanguang.(2015).POWER-LAW DISTRIBUTIONS BASED ON EXPONENTIAL DISTRIBUTIONS: LATENT SCALING, SPURIOUS ZIPF'S LAW, AND FRACTAL RABBITS.FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY.
MLA	Chen, Yanguang."POWER-LAW DISTRIBUTIONS BASED ON EXPONENTIAL DISTRIBUTIONS: LATENT SCALING, SPURIOUS ZIPF'S LAW, AND FRACTAL RABBITS".FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY (2015).