| APPROXIMATE REPRESENTATION OF THE p-NORM DISTRIBUTION |
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| 作者姓名： | SUN Haiyan |
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| 作者单位： | Ph.D,Professor,School of Geodesy and Geomatics,Wuhan University,129 L uoyu Road,
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| 基金项目： | ProjectsupportedbytheSustentationPlanforOutstandingTeachersofAd
vancedCollegesbyMinistryofEducationandtheScientificResearchFundof
WuhanUniversity. |
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| 摘 要： | 1 ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｓｕｒｖｅｙｉｎｇｄａｔａｐｒｏｃｅｓｓｉｎｇ ,ｉｔｉｓｏｆｔｅｎｓｕｐｐｏｓｅｄｔｈａｔｏｂｓｅｒｖａｔｉｏｎａｌｅｒｒｏｒｓｄｉｓｔｒｉｂｕｔｅｎｏｒｍａｌｌｙ .Ｉｆｏｂ ｓｅｒｖａｔｉｏｎｓｃｏｍｅｆｒｏｍｔｈｅｎｏｒｍａｌｄｉｓｔｒｉｂｕｔｉｏｎａｌｃｌａｓｓ ,ｔｈｅｍｅｔｈｏｄｏｆｌｅａｓｔｓｑｕａｒｅｓｃａｎｇｉｖｅｔｈｅｍｉｎｉ＿ＰｒｏｊｅｃｔｓｕｐｐｏｒｔｅｄｂｙｔｈｅＳｕｓｔｅｎｔａｔｉｏｎＰｌａｎｆｏｒＯｕｔｓｔａｎｄｉｎｇＴｅａｃｈｅｒｓｏｆＡ…
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APPROXIMATE REPRESENTATION OF THE p_NORM DISTRIBUTION |
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| SUN Haiyan.APPROXIMATE REPRESENTATION OF THE p-NORM DISTRIBUTION[J].Geo-Spatial Information Science,2001,4(3). |
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| Authors: | Sun Haiyan |
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| Abstract: | In surveying data processing,we generally suppose that the observatio nal errors distribute normally.In this case the method of least squares can giv e the minimum variance unbiased estimation of the parameters.The method of leas t squares does not have the character of robustness,so the use of it will becom e unsuitable when a few measurements inheriting gross error mix with others.W e can use the robust estimating methods that can avoid the influence of gross er rors.With this kind of method there is no need to know the exact distr ibution of the o bservations.But it will cause other difficulties such as the hypothesis tes ting for estimated parameters when the sample size is not so big.For non_normal ly distributed measurements we can suppose they obey the p_norm distribution law.The p_norm distribution is a distributional class,which includes the mo st frequently used distributions such as the Laplace,Normal and Rectangular ones .This distribution is symmetric and has a kurtosis between 3 and -6/5 when p is larger than 1.Using p_norm distribution to describe the statistica l char acter of the errors,the only assumption is that the error distribution is a symm etric and unimodal curve. This method possesses the property of a kind of self_ad apting.But the density function of the p_norm distribution is so complex tha t it makes the theoretical analysis more difficult.And the troublesome calculati on also makes this method not suitable for practice.The research of this paper i ndicates that the p_norm distribution can be represented by the linear combi nation of Laplace distribution and normal distribution or by the linear combinat ion of normal distribution and rectangular distribution approximately.Which kind of representation will be taken is according to whether the parameter p is larger than 1 and less than 2 or p is larger than 2.The approximate d i stribution have the same first four order moments with the exact one.It mean s that approximate distribution has the same mathematical expectation,variance,s kewness and kurtosis with p_norm distribution.Because every density function use d in the approximate formulae has a simple form,using the approximate density fu nction to replace the p_norm ones will simplify the problems of p_norm d istributed data processing obviously. |
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| Keywords: | p _norm distribution approximate representation of the p _norm distribution skewness kurtosis |
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