Andréhette Verster

Analysis of the same day of the week increases in peak electricity demand in South Africa

Modelling of the same day of the week increases in peak electricity demand using the Generalized Pareto-type (GP-type) distribution is discussed. The GP-type distribution discussed in this paper has one parameter to estimate and as such, it is referred to as the Generalized Single Pareto (GSP). The data is from Eskom, South Africas power utility company and is for the years 2000 to 2011. A comparative analysis is done with a Generalized Pareto Distribution (GPD). Although both the GSP and the GPD fit the data, the use of the GSP is easier since it has only one parameter to estimate instead of two as is the case with the GPD. Modelling of the same day of the week increases in peak electricity demand improves the reliability of a power network if an accurate assessment of the level and frequency of future extreme load forecasts is carried out.

Modelling high river flows and Southern Oscillation Index jointly

It has been pointed out in the article by de Waal (de Waal, D.J., 2009. Posterior predictions on river discharges. In: M.J. Kallen and S.P. Kuniewski, eds. Risk and decision analysis in maintenance optimization and flood management. Amsterdam: IOS Press, Delft University Press) in honour of the late Jan van Noortwijk that the annual volume of inflow to the Gariep Dam can be predicted to some extent by the October Southern Oscillation Index (SOI). It was shown that the larger the index, the higher the volume of water that can be expected. The variation on high inflows increases, and it is important for ESKOM that generates hydropower at the dam wall to make maximal use of the water and to prevent spillage over the wall. This makes it necessary to investigate the upper tail dependency between inflow and SOI. This article investigates the annual volume of stream flow of the Orange river and October SOI jointly through the Gumbel copula due to upper tail dependence. The tail-dependence coefficient η is estimated from its posterior density under the Pareto type distribution assumed on T = min(Z 1, Z 2) given η where Zi , i = 1, 2 are the Fréchet transforms of the observed variables.

A Truncated Pareto Model to Estimate the Under Recovery of Large Diamonds

The metallurgical recovery processes in diamond mining may, under certain circumstances, cause an under-recovery of large diamonds. In order to predict high quantiles or tail probabilities we use a Bayesian approach to fit a truncated Generalized Pareto Type distribution to the tail of the data consisting of the weights of individual diamonds. Based on the estimated tail probability, the expected number of diamonds larger than a specified weight can be estimated. The difference between the expected and observed frequencies of diamond weights above an upper threshold provides an estimate of the number of diamonds lost during the recovery process.