Scholarly record

THE PROBABILITY DISTRIBUTION FUNCTION OF THE ABSOLUTE SECTION DISCREPANCIES IN THE THIRD LEVELLING OF BULGARIA

Vasil Cvetkov

Abstract

The statistical characteristics of section discrepancies and standardized section discrepancies derived from the Third Levelling of Bulgaria are examined in detail. The computed excess kurtosis values are minus 0.44 and minus 0.56, respectively, with standard deviations of 0.07. These results clearly indicate a notable departure from the normal distribution, for which the excess kurtosis is equal to zero. This finding suggests that the conventional methodology for defining permissible limits between measurements, traditionally based on the Gaussian law of error propagation and uncertainty accumulation, is not fully adequate in this case. Continued reliance on this assumption may result in the acceptance of measurements containing significant errors, as well as the unjustified rejection of valid observations. Furthermore, such limitations have important implications for the design and optimization of high-precision geometric levelling networks, including national reference systems and deformation monitoring frameworks. The analysis also reveals that the skewness of both datasets is approximately 0.09, with a standard deviation of 0.07, indicating that the distributions are nearly symmetric, though not perfectly centered. In light of these statistical properties, the application of Pearson’s system of frequency curves is proposed as a more appropriate approach for modeling the empirical distributions of absolute section discrepancies and their standardized counterparts. The results demonstrate that Pearson Type I distributions can effectively describe both quantities. For practical implementation, the associated probability density functions are approximated using polynomial representations. On this basis, statistically justified, probability-driven limits for section discrepancies are formulated, providing a more reliable framework for quality control in levelling networks.

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