Probability density function and estimation for error of digitized map coordinates in GIS①
来源期刊：中南大学学报(英文版)2004年第1期
论文作者：童小华 刘大杰
文章页码：69 - 74
Key words：probability density function; distribution fitness test; leastp-norm estimation
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 thep-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 andp-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-squareχ2test and Kolmogorov test for digitized data are conducted. The results show that the error in map digitization obeys thep-norm distribution whose parameter is close to 1.60. A leastp-norm estimation and the least square estimation of digitized data are further analyzed, showing that the leastp-norm adjustment is better than the least square adjustment for digitized data processing in GIS.
