An application of theoretical probability distributions, to the study of PM10 and PM2.5 time series in Athens, Greece

Probability density functions (pdf) have been used in the analysis of the distribution of
pollutant data, for examining the frequency of high concentration events. There have been
very few studies on the concentration distribution of PM in urban areas. The distribution of PM
concentrations has an impact on human health effects and the setting of PM regulations.
Eight probability distribution functions were fitted to measured concentrations of PM10 and
PM2.5 in order to determine the shape of the concentration distribution. The “goodness-of-fit”
of the probability density functions, to the data, was evaluated, using various statistical indices
(including Chi-square and Kolmogorov-Smirnov tests). The evaluation was conducted for two
separate years and the results indicated that the Pearson type VI pdf provided a better fit to
the measured data. Other functions exhibiting high accuracy of fit were the inverse Gaussian,
the lognormal and Pearson type V.
The possibility to use probability density functions for predicting the daily high concentration
percentiles to less than everyday sampling scenarios is also shown. The differences in the
distribution of concentrations under these scenarios are important for regulatory compliance.
When trying to detect the high concentrations there is significant possibility of missing the
events and thus, underestimating the number of exceedances occurred. Significant deviations
from actual daily measurements of PM10 and PM2.5 concentration percentiles were observed,
when infrequent sampling scenarios were examined. The differences were higher for the 1-in-
6 sampling schedules and reached 2.8% for mean PM10 and 8% for PM2.5 while for the
maximum concentrations the respective differences were 21.3% and 31.9%. Differences
between the frequency distributions of everyday and non-everyday sampled concentrations
were observed, while lognormal and inverse Gaussian functions provided a better
approximation of the upper percentiles.
Fitting infrequent data on continuous probability functions for the improvement of the
approximation to the real statistical values provided good results regarding the 90th percentile,
which corresponds to the E.U. provision of 35 annual exceedances of 24-h limit PM10 values.
In the case of the extreme 98th and 99th percentiles, the method provided satisfactory results
for both the PM10 infrequent sampling scenarios.