Abstract
Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in GIS does not obey the normal distribution but the p-norm distribution with a determinate parameter. Assuming that the error is random and has the same statistical properties, the probability density function of the normal distribution, Laplace distribution and p-norm distribution are derived based on the arithmetic mean axiom, median axiom and p-median axiom, which means that the normal distribution is only one of these distributions but not the least one. Based on this idea, distribution fitness tests such as Skewness and Kurtosis coefficient test, Pearson chi-square x 2 test and Kolmogorov test for digitized data are conducted. The results show that the error in map digitization obeys the p-norm distribution whose parameter is close to 1.60. A least p-norm estimation and the least square estimation of digitized data are further analyzed, showing that the least p-norm adjustment is better than the least square adjustment for digitized data processing in GIS.
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Foundation item: Project (40301043 and 40171078) supported by the National Natural Science Foundation of China and Project supported by Visiting Scholar Foundation of Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing Wuhan University, China
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Tong, Xh., Liu, Dj. Probability density function and estimation for error of digitized map coordinates in GIS. J Cent. South Univ. Technol. 11, 69–74 (2004). https://doi.org/10.1007/s11771-004-0015-4
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DOI: https://doi.org/10.1007/s11771-004-0015-4