Maseka Lesaoana

Investigating the goodness-of-fit of ten candidate distributions and estimating high quantiles of extreme floods in the lower Limpopo River Basin, Mozambique

Abstract We compare ten candidate distributions for their goodness-of-fit in modelling the annual maximum daily flood heights in the lower Limpopo River Basin, Mozambique. The ten candidate distributions compared in this study are Generalised Gamma (GG), two-parameter Gamma, three-parameter Gamma, two-parameter lognormal, three-parameter lognormal, log-Pearson Type 3 (LP3), Generalised Extreme Value (GEV), two-parameter Weibull, three-parameter Weibull, and Gumbel distribution. The GEV, Gumbel, and GG were the best three distributions at Sicacate based on their ability to model the tails. The three-parameter Gamma, three-parameter lognormal and GEV were the best three distributions at Chokwe. Among the parameter estimation methods used were the maximum likelihood method and the method of L-moments. Goodness-of-fit was evaluated by means of Kolmogorov-Smirnov and Anderson-Darling tests, as well as P-P plots and simulation studies to check whether the distribution could mimic the observed values. Results of the expected return periods and probable high quantiles at both sites Chokwe (upstream) and Sicacate (downstream) indicated that the 13 m flood height of the year 2000 was way higher than the 100-year-flood height and had a return period in excess of 250 years based on the best fitting distributions, implying that it has a very small likelihood of being equalled or exceeded at least once in 250 years.

Investigating the effects of different grazing ratios and stocking rate of cattle and goats under mixed-species grazing on different plant species

The study focused on investigating the effects of different grazing ratios and stocking rate of cattle and goats under mixed species grazing on different species of plant. The experimental site was Matopos Research Station farm in Zimbabwe. This study was confined to the commonest grass species and forbs at the experimental site. Treatments spanned a period of eight years; from 1999 to 2007. Generally, heavy goats stocking rate resulted in low productivity of browse biomass while heavy cattle stocking rate resulted in low herbaceous biomass productivity. The present results do not support existence of a linear relationship between herbaceous biomass productivity and annual rainfall. Rather, a quadratic relationship existed, suggesting that there might be other factors in addition to rainfall that accounted for biomass productivity. Grazing ratios and stocking rate of cattle and goats, year and their interactions affected the productivity of plant species in the rangeland. Finally, farmers are encouraged to practice mixed-species grazing at an optimal grazing ratio of 4 cattle and 36 goats per 20 ha of rangeland.

Non-Linearities, Structural Breaks and Fractional Integration in the Analysis of the Ghanaian and the South African CPI Inflation Rates

Keeping a low steady rate of inflation is one of the government’s most important responsibilities. Inflation is an important determinant of economic growth. Consequently, it has been one of the most examined areas in economics, from both theoretical and empirical perspectives. Indeed, economists have shown continued interest in this essential economic variable. The most important question related to inflation is: Does non-linearity exist in inflation? The answer to this question, which has important policy implications, can support or endanger the validity of several important economic models. Hence, a clear understanding of the changing aspects of inflation is crucial to any economy because it is regarded as a significant variable in a number of economic models, whose legitimacy critically relies on whether or not this variable is stationary. In practice, many economic time series models rely on linearity. Nonetheless, it has often been found that simple linear time series models regularly leave certain aspects of economic and financial data inexplicable. This paper proposes a model that combines fractional integration with non-linear deterministic terms based on the Chebyshev polynomials in time for the analysis of CPI inflation rates of Ghana and South Africa in Sub-Saharan Africa. Firstly, we tested for non-linear deterministic terms in the context of fractional integration. The estimates of the differencing parameter, d, were found to be 1.11 and 1.32, respectively for the Ghanaian and the South African inflation rates, but the non-linear trends were found to be statistically insignificant in the two series. A linear model was then investigated and the results indicated that the order of integration for the Ghanaian inflation series was slightly above 1. However, for the case of South Africa, a cyclical I(d) process was found to be more appropriate, with an order of integration below 1, thus showing mean reversion and a cyclical structure of approximately 80 periods (months) per cycle. The implication of these findings could assist in a decision-making process regarding adjusting monetary policy instruments such as inflation targeting (IT) or adopting different monetary policies, to achieve the desired target.

Modelling non-stationary annual maximum flood heights in the lower Limpopo River basin of Mozambique

In this article we fit a time-dependent generalised extreme value (GEV) distribution to annual maximum flood heights at three sites: Chokwe, Sicacate and Combomune in the lower Limpopo River basin of Mozambique. A GEV distribution is fitted to six annual maximum time series models at each site, namely: annual daily maximum (AM1), annual 2-day maximum (AM2), annual 5-day maximum (AM5), annual 7-day maximum (AM7), annual 10-day maximum (AM10) and annual 30-day maximum (AM30). Non-stationary time-dependent GEV models with a linear trend in location and scale parameters are considered in this study. The results show lack of sufficient evidence to indicate a linear trend in the location parameter at all three sites. On the other hand, the findings in this study reveal strong evidence of the existence of a linear trend in the scale parameter at Combomune and Sicacate, whilst the scale parameter had no significant linear trend at Chokwe. Further investigation in this study also reveals that the location parameter at Sicacate can be modelled by a nonlinear quadratic trend; however, the complexity of the overall model is not worthwhile in fit over a time-homogeneous model. This study shows the importance of extending the time-homogeneous GEV model to incorporate climate change factors such as trend in the lower Limpopo River basin, particularly in this era of global warming and a changing climate.

Application of multinomial logistic regression to educational factors of the 2009 General Household Survey in South Africa

This paper combines factor analysis and multinomial logistic regression (MLR) in understanding the relationship between extracted factors of quality of life pertaining to education and variables of five key areas of the levels of development in the context of the South African 2009 General Household Survey. MLR was used to analyse the identified educational factors from factor analysis. It was also used to determine the extent to which these factors impact on educational level outcomes across South Africa. The overall classification accuracy rate displayed was 73.0% which is greater than the proportion by chance accuracy criteria of 57.0%. This means that the model improves on the proportion by chance accuracy rate of 25.0% or more so that the criterion for classification accuracy is satisfied and the model is adequate. Evidence is that being historically disadvantaged, absence of parental care, violence in schools and the perception that fees were too high generally have a negative influence on educational attainment. The results of this paper compare well with other household surveys conducted by other researchers.

A Minimum Spanning Tree Approximation to the Routing Problem through 'K' Specified Nodes

Abstract This paper presents a minimum spanning tree approach to determine a route through ‘k’ specified nodes. The path through ‘k’ specified nodes is a difficult problem for which no good solution procedure is known. The proposed method determines the route, which may be either an optimal or a near optimal path.

A transportation branch and bound algorithm for solving the generalized assignment problem

AbstractThis paper presents a transportation branch and bound algorithm for solving the generalized assignment problem. This is a branch and bound technique in which the sub-problems are solved by the available efficient transportation techniques rather than the usual simplex based approaches. A technique for selecting branching variables that minimize the number of sub-problems is also presented.