Quantifying South Africa’s sulphur dioxide emission efficiency in coal-powered electricity generation by fitting the three-parameter log-logistic distribution

Maseapei Elizabeth Girmay, Delson Chikobvu


This paper fits the three-parameter log-logistic (3LL) distribution to sulphur dioxide (SO2) monthly emissions in kilograms per gigawatt hour (kg/GWh) and in milligrams per cubic nano metre (mg/Nm3), at 13 of Eskom’s coal fired power-generating stations in South Africa. The aim is to quantify and describe the emission of sulphur dioxide at these stations using a statistical distribution, and to also estimate the probabilities of extreme emissions and exceedances (emissions above a certain threshold). Using the 3LL distribution is proposed as such a distribution. The log-logistic distribution is a special form of a Burr-type distribution. Various goodness-of-fit measures, including the Kolmogorov Smirnov, the Anderson Darling and some graphical tests, are employed to test if the 3LL distribution is a good fit to the data. The maximum likelihood method is used to estimate the parameters. The distribution fit is important as it then becomes possible to quantify and manage the SO2 emissions effectively. The 3LL distribution, which is compared with three other distributions, gave the best overall fit to most of the power stations.


Keywords: emission, Eskom, log logistic distribution, goodness of fit, sulphur dioxide, Burr-type distribution

  • Quantification of SO2 emissions in terms of a statistical distribution
  • Calculating the probability of SO2 emissions exceeding certain specified limits
  • Ranking power stations in terms of SO2 emissions efficiency


emission, Eskom, log logistic distribution, goodness of fit, sulphur dioxide, Burr-type distribution

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DOI: http://dx.doi.org/10.17159/2413-3051/2017/v28i1a1530


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