干旱区生态环境知识资源中心(Arid): Usability of the Benford's law for the results of least square estimation

Arid

DOI	10.1007/s40328-019-00259-3
	Usability of the Benford's law for the results of least square estimation
	Tunalioglu, Nursu; Erdogan, Bahattin
通讯作者	Tunalioglu, Nursu
来源期刊	ACTA GEODAETICA ET GEOPHYSICA
ISSN	2213-5812
EISSN	2213-5820
出版年	2019
卷号	54 期号:3 页码:315-331
英文摘要	Benford's law (BL), also known as the first-digit or significant-digit law, is an intriguing pattern in data sets, considers the frequency of occurrence of the first digits, which are not uniformly distributed as might be expected, conversely follow a specified theoretical distribution. According to BL, the occurrence of first non-zero digit in a numerical data, which is generated or found in nature, depends on a logarithmic distribution. Least square estimation (LSE) method is mostly preferred for the estimation of the unknown parameters from different types of geodetic data. The residuals and the normalized residuals of the LSE method, which follow normal distribution and expected values of them are zero are used in outlier detection problem. In this study, BL is investigated for residuals and the normalized residuals estimated from LSE method. Three types of geodetic data are used: (1) simulated regression models, (2) global positioning system (GPS) data, (3) leveling network. The first group data sets are simulated based on linear regression and univariate models and each simulated group is generated for a number of 100, 1000, and 10,000 samples. To generate second group, an international global navigation satellite system (GNSS) service (IGS) station data (ISTA) is processed by kinematic PPP approach using GIPSY OASIS II v6.4 software. Here, the observation duration of GPS data is 4 days. For the last data, a leveling network with 55 points involving 110 observations of height differences is simulated. BL has been applied to the residuals (v) and normalized residuals (w) estimated from LSE method. Goodness-of-fit test has been implemented to determine whether a population has a specified BL distribution or not. This test is based on how good a fit we have between the frequency of occurrence of residuals and normalized residuals in an observed sample and the expected frequencies obtained from the hypothesized distribution. The results depending on the statistical test show that each data set (residuals and normalized residuals) used in this study follows BL.
英文关键词	Benford's law Frequency of occurrence Residuals and normalized residuals Goodness-of-fit test Least square estimation
类型	Article
语种	英语
国家	Turkey
收录类别	SCI-E
WOS记录号	WOS:000484615900001
WOS关键词	LEADING DIGITS
WOS类目	Geochemistry & Geophysics
WOS研究方向	Geochemistry & Geophysics
资源类型	期刊论文
条目标识符	http://119.78.100.177/qdio/handle/2XILL650/213837
作者单位	Yildiz Tech Univ, Civil Engn Fac, Dept Geomat Engn, Istanbul, Turkey
推荐引用方式 GB/T 7714	Tunalioglu, Nursu,Erdogan, Bahattin. Usability of the Benford's law for the results of least square estimation[J],2019,54(3):315-331.
APA	Tunalioglu, Nursu,&Erdogan, Bahattin.(2019).Usability of the Benford's law for the results of least square estimation.ACTA GEODAETICA ET GEOPHYSICA,54(3),315-331.
MLA	Tunalioglu, Nursu,et al."Usability of the Benford's law for the results of least square estimation".ACTA GEODAETICA ET GEOPHYSICA 54.3(2019):315-331.