Faculty of Natural and Agricultural Sciences
School of Mathematical Sciences
Department of Statistics
Selected Highlights from Research Findings
Optimal statistical techniques for the analysis of multivariate grouped data, that is only available in grouped format or observed in interval format, were developed. These inferential procedures were applied to develop statistical models in cases like the distribution of income and expenditure, premium and age.
Optimale statistiese tegnieke vir die analise van meervariante gegroepeerde data, wat slegs in gegroepeerde vorm beskikbaar is of in intervalformaat waargeneem is, is ontwikkel. Hierdie inferensiële prosedures word aangewend om statistiese modelle in gevalle soos die distribusie van inkomste- en uitgawe, premie en ouderdom te ontwikkel.
Contact person: Prof NAS Crowther.
Time series research activities were focused mainly in the areas of finance, econometrics and industry. An investigation into models and methods used to deal with specific properties of financial time series was carried out. In the field of econometrics, a study of the memory properties of the forward premium in the South African context was undertaken and tests were developed to establish to which extent purchasing power parity exists between South Africa and its trading partners. Models were proposed for time series with cyclical patterns, such as traffic volume, electricity demand and telecommunication utilization.
Die fokus van tydreeksnavorsingsaktiwiteite is hoofsaaklik in die finansiële, ekonometriese en industriële gebied. Modelle en metodes wat ontwerp is om voorsiening te maak vir die kenmerkende eienskappe van finansiele tydreekse is bestudeer. 'n Studie is onderneem om die geheue eienskappe van die termynpremie binne die Suid-Afrikaanse konteks te ondersoek en toetse is uitgevoer om te bepaal tot welke mate koopkragpariteit tussen Suid-Afrika en sy handelsvennote bestaan. Modelle is voorgestel vir tydreekse met sikliese patrone, soos vervoervolume, vraag na elektrisiteit en die benutting van telekommunikasiebronne.
Contact person: Dr H Boraine.
Finding the small sample distribution of a one-sample linear rank statistic under the alternative hypothesis, or under the nullhypothesis without necessarily assuming symmetry, has always been prohibitive, due to the complexity of the underlying mathematics. In this research it was shown how the concept of the probability generating function and a computer algebra package Mathematica can be used to overcome this problem.
Bepaling van die kleinsteekproefverdeling van 'n eensteekproef lineêre rangstatistiek onder die alternatiewe hipotese, of onder die nulhipotese sonder dat simmetrie noodwendig aanvaar word, was altyd beperk, as gevolg van die kompleksiteit van die onderliggende wiskunde. In hierdie navorsing is met behulp van die begrip van waarskynlikheidsvoortbringende funksie en 'n rekenaaralgebrapakket, Mathematica, aangetoon hoe hierdie prbleem oorbrug kan word.
Contact person: Prof CF Smit.
A general methodology for the statistical analysis of grouped survival data of long- and shortterm policies in the insurance industry has been developed. This forms the statistical foundation for scientific decisionmaking with respect to actuarial design, maintenance and marketing of insurance policies. Although the methodology was developed specifically for the insurance industry, it may be applied to any survival model where the survival times of people or objects have to be characterized.
'n Algemene metodologie vir die statistiese analise van gegroepeerde oorlewingsdata van lang- en korttermyn polisse in die versekeringsbedryf is ontwikkel. Dit vorm die statistiese grondslag vir wetenskaplike besluitneming met betrekking tot aktuariële ontwerp, onderhoud en bemarking van versekeringspolisse. Alhoewel die metodologie spesifiek vir die versekeringsbedryf ontwikkel is, kan dit op enige oorlewingsmodel, waar die oorlewingstye van mense of voorwerpe gekarakteriseer moet word, toegepas word.
Contact person: Dr EM Louw.
A method was developed for the statistical analysis of categorical data where information on some of the variables considered is missing at random. The computation involved in this method is less intensive than that currently used in practice. This provides a technique for the analysis of incomplete tables.
'n Metode is ontwikkel vir die statistiese analise van kategoriese data waar inligting vir sekere van die veranderlikes onder beskouiing ewekansig nie waargeneem is nie. Die berekeninge hierby betrokke is minder intensief as wat tans in die praktyk gebruik word en bied 'n tegniek vir die analise van onvolledige tabelle.
Contact person: Ms R Ehlers.
The estimation of the truncation point of the two parameter exponential distribution was studied. The asymptotic behavior and properties of fixed width estimation procedures under the deviation model reflect the robustness characteristics of such procedures and lead to the definition of more robust procedures. The identification and use of animals with high genetic potential in breeding programs have huge commercial value. Statistical procedures, which estimate and predict genetic potential, should not heavily be influenced by deviations from the assumption base. Numerous studies investigate and describe the robustness expectations of procedures. The effect of selection of best animals, differences between genetic base levels, and the distribution of the random component on the estimation of genetic values is described. The value of remedial steps were highlighted.
Die beraming van die afknotingspunt van die tweeparameter eksponensiaalverdeling word ondersoek. Die asymtotiese gedrag en eienskappe van vastelengte vertrouingsinterval beramingsprosedures onder die afwykingsmodel reflekteer die robuustheid eienskappe van sulke prosedures en gee aanleiding tot die definiëring van meer robuuste tegnieke. Die identifisering en gebruik van diere van hoë genetiese potensiaal in teeltprogramme het groot kommersiële waarde. Statistiese prosedures wat genetiese potensiaal beraam en voorspel behoort min beïnvloed te word deur afwykings vanaf die aannamebasis. In verskeie studies is hierdie robuustheid verwagting van prosedures ondersoek en beskryf. Die effek van selektering van top diere, verskille tussen genetiese basisvlakke, en die verdeling van die stogatiese komponente op beraamde genetiese waarde is beskryf. Die waarde van remediërende stappe word uitgewys.
Contact person: Dr FHJ Kanfer.
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