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Analysis of the distribution of statistical concentrations of pollutants in samples of treated wastewater from small sewage treatment plants

Kaczor Grzegorz B.

Journal of Water and Land Development

2022

no. 55

115--124

The aim of the research was to show which theoretical statistical distribution best reflects and describes the variability of pollutant concentrations in treated sewage, discharged from small sewage treatment plants, characterised by a value below 2000 PE. The statistical analysis additionally takes into account the influence of the number of measuring sequence data on the shape and level of the distribution fit. The data for the research were obtained from three small sewage treatment plants, operating in the Lesser Poland, 10, 11 and 14 km from Kraków. Due to their size, these facilities are included in the group of treatment plants below 2000 PE. The research was conducted for 10 years. In the statistical analysis, 20-, 40-, 60- and 80-element data series were used, including the values of biochemical oxygen demand (BOD5), chemical oxygen demand (CODCr) and total suspended solids (TSS), determined in samples of treated wastewater. Two commonly used tests, Kolmogorov-Smirnov λ and Pearson’s χ2 test were used to assess the fit of the theoretical statistical distribution to the empirical data distribution. Statistical analysis showed that the studied communities were characterised by an asymmetric, right-oblique distribution. Most often, the empirical distribution of the analysed measurement sequences was consistent with the Fisher-Tippett distribution. On the basis of the χ2 test, this distribution was described by a total of 31 out of 36 analysed groups at the significance level of a = 0.05. Other distributions that often describe the analysed empirical data are: Gamma, log-normal, Chi-square, and Weibull. The common feature of these distributions is usually asymmetry, right oblique. The skewness value ranges from 0.15 to 1.69.