MP estimation applied to platykurtic sets of geodetic observations

• Main Author: Wiśniewski Zbigniew
• Format: Article
• Language: English
• Published: Polish Academy of Sciences 2017-06-01
• Series: Geodesy and Cartography
• Subjects: M and MP estimation; platykurtic probabilistic models; Pearson’s distributions
• Online Access: http://www.degruyter.com/view/j/geocart.2017.66.issue-1/geocart-2017-0001/geocart-2017-0001.xml?format=INT

MP estimation is a method which concerns estimating of the location parameters when the probabilistic models of observations differ from the normal distributions in the kurtosis or asymmetry. The system of Pearson’s distributions is the probabilistic basis for the method. So far, such a method was applied and analyzed mostly for leptokurtic or mesokurtic distributions (Pearson’s distributions of types IV or VII), which predominate practical cases. The analyses of geodetic or astronomical observations show that we may also deal with sets which have moderate asymmetry or small negative excess kurtosis. Asymmetry might result from the influence of many small systematic errors, which were not eliminated during preprocessing of data. The excess kurtosis can be related with bigger or smaller (in relations to the Hagen hypothesis) frequency of occurrence of the elementary errors which are close to zero. Considering that fact, this paper focuses on the estimation with application of the Pearson platykurtic distributions of types I or II. The paper presents the solution of the corresponding optimization problem and its basic properties.