For this project, a historical statistical analysis of the Amplitude of Mass Fluctuations ($\sigma_8$) and Hubble's Constant ($H_0$) parameters in the Standard Cosmological Model was carried out to determine whether or not the given error bars truly represent the dispersion of values. It was found through analysis of the Chi-Squared ($\chi^2$) values of the data that for $\sigma_8$ (60 data points and $\chi^2$ between 183.167 and 189.037) that the associated probability Q is extremely low, with $Q = 1.5597*10^{-15}$ for the weighted average and $Q = 1.2107*10^{-14}$ for the best fit of the data. This was also the case for the $\chi^2$ values (163 data points and $\chi^2$ between 484.3977 and 575.655) of $H_0$, where $Q = 4.2176*10^{-34}$ for the linear fit of the data and $Q = 1.0342*10^{-47}$ for the weighted average of the data. Through further analysis, it is shown in question, a linear fit is a better estimate of the data than the weighted average. The general conclusion is that the statistical error bars have been underestimated (in around 20\% of the measurements), or the systematic errors were not properly taken into account.

Mehr als zwei Drittel der Menschen unterhalb der Armutsgrenze in Sub-Sahara Afrika leben im ländlichen Raum; vier Fünftel von ihnen erwirtschaften ihren Lebensunterhalt überwiegend durch landwirtschaftliche Aktivitäten. Somit spielt die Landwirtschaft eine herausragende Rolle in der ländlichen Wirtschaftsentwicklung und Armutsbekämpfung. Dem Sektor kam in der letzten Dekade wieder gestiegene Aufmerksamkeit durch Ent-wicklungsforschung und Entwicklungszusammenarbeit zu. Jedoch ist der Zusammen-hang zwischen landwirtschaftlichen Aktivitäten und ihrem Beitrag zur Überwindung der Armut auf der Haushaltsebene („poverty exit”) kaum empirisch analysiert. In Kenia trägt der Agrarsektor 26 % zum BIP bei, vor- und nachgelagerten Bereiche zusätzliche 27 %. Mehr als 70 % der ländlichen Bevölkerung arbeiten in der Landwirt-schaft; landesweit sind das mehr als 40 % der Gesamtbevölkerung. Seit der Jahrtau-sendwende ist der Sektor im Durchschnitt um 3 % gewachsen, allerdings mit hoher Varianz. Seitdem haben sich viele kleinbäuerliche Haushalte in landwirtschaftliche Wert-schöpfungsketten wie Exportgemüse oder Milch integriert. Gleichzeitig sank die ländli-che Armutsrate von 49,7 % auf 40,1 %. Was also war der Beitrag der Wertschöpfungs-kettenentwicklung auf die ländliche Armutsreduktion? Diese Arbeit untersucht am Beispiel Kenias, warum manche ländlichen Haushalte die Armut überwunden haben und welche landwirtschaftlichen Aktivitäten dazu geführt haben. Die Basis dafür bilden drei unterschiedliche Stränge in der Literatur: die Pro-Poor Growth-Debatte, die Wertschöpfungskettenliteratur, und die Armutsforschung entlang des sogenannten „Q-Squared Paradigms“. Elemente dieser drei Stränge bilden das analy-tische Gerüst für die empirische Analyse im ländlichen Kenia und kombinieren quanti-tative und qualitative Methoden. Zuerst wurde das ländliche Haushaltpanel „TAMPA“ mit 1275 ländlichen Haushalten über einen Zeitraum von 10 Jahren (1997-2007) nach Haushalten ausgewertet, die die Armut überwunden haben. Eine Stichprobe von 51 dieser Haushalte wurde im Jahr 2010 nachbefragt, um die spezifischen Gründe für den wirtschaftlichen Aufstieg zu analysieren. Die Ergebnisse dieser Befragung lassen sich auf zwei Ebenen interpretieren und leisten daher zwei unterschiedliche Beiträge zur ländlichen Armutsforschung: erstens methodi-sche Hinweise zur Datenerfassung und -interpretation ländlicher Haushaltspanele in Afrika; zweitens Erkenntnisse zu effektiven Strategien, wie die Integration in landwirt-schaftliche Wertschöpfungsketten zur Überwindung ländlicher Armut führen kann. Das zentrale methodische Ergebnis liegt darin, dass obwohl die quantitativen Daten von vier Haushaltsbefragungen im Rahmen des Panels eindeutig eine Überwindung der Armut bei allen 51 Haushalten zeigen, nur 25 dieser Haushalt tatsächlich der Armut entkommen sind. Die anderen 26 Haushalte haben sich unterschiedlich entwickelt oder sind Messfehlern unterlegen. Die Lebensgeschichten („life histories“) der 25 Haushalte, die die Armut überwunden hatten, zeigen jedoch eindeutig, dass die Integration in landwirtschaftliche Wertschöpfungsketten tatsächlich einen sehr guten Entwicklungs-pfad aus der Armut bieten kann, wenn die landwirtschaftlichen Aktivitäten produktiv und marktorientiert sind und Investitionen und Innovationsadoption erfahren. Die Mischung aus Spezialisierung auf eine kommerzielle Wertschöpfungskette, die Elemente kollektiver Vermarktungsstrukturen wie Kooperativen aufweist, einerseits und risikomi-nimierender Diversifizierung inklusive ernährungsrelevantem Eigenkonsum anderer-seits, scheint hierbei der erfolgreichste Weg aus der ländlichen Armut zu sein. Beide Ergebnisbereiche führen zu Schlussfolgerungen, wie zukünftig landwirtschaftliche Wertschöpfungskettenförderung den Fokus auf Armutsreduzierung stärken kann und wie die Armutsforschung die Umsetzung solcher Projekte und deren Armutseffekte besser messen könnte.:1 INTRODUCTION 2 POVERTY AND GROWTH DEBATES AND THEIR IMPLICATIONS FOR AID TO AGRICULTURE 3 POVERTY DYNAMICS AND POVERTY EXITS: CONCEPTS, METHODOLOGIES AND CASES STUDIES 4 EMPIRICAL EVIDENCE: POVERTY EXITS IN RURAL KENYA 5 CONCLUSIONS AND RECOMMENDATIONS / In Sub-Saharan Africa, more than two thirds of the poor live in rural areas and four out of every five households are making a living predominantly based on agricultural and livestock activities. Agriculture plays a major role in stimulating rural economic development and in driving rural households out of poverty. Hence, the sector experienced a revival in development cooperation and devel-opment research during the past decade. However, it is rarely analysed which agricultural strategies rural households undertake to successfully exit poverty. In Kenya, agriculture is key to the economy, contributing 26 % of the GDP di-rectly and another 27 % indirectly. The sector provides employment for more than 40 % of the total population and more than 70 % of the rural population. Since the Millennium, the sector experienced an average growth rate of 3 % per year, albeit high variances. Since then, many small-scale farmers in Kenya have integrated their economic activities into agricultural value chains, such as food crops, export horticulture or dairy. At the same time, rural poverty incidence re-duced from 49.9 % to 40.1 %, but is still significantly higher than urban poverty. So what was the impact of value chain development on rural poverty reduction? This research analyses why some rural households exited poverty and to what extent these poverty exits are explained by their agricultural activities. Based on a literature review of the pro-poor growth debate, of agricultural value chain de-velopment and of poverty research along the ‘q-squared-paradigm', the results from three different schools are combined for the design of an empirical field survey in rural Kenya applying quantitative and qualitative methods. First, the ten-year TAMPA panel data set for 1275 rural households was analysed for the identification of poverty exiting households. These poverty exiters were then sampled again for qualitative follow-up interviews in order to specifically analyse their explanation for their upward mobility. 51 households were visited and in-terviewed for their agricultural life history in 2010. The results are two-fold: first, even though the four wave panel data for all 51 households showed a clear upward trend, only 25 households turned out to have actually exited poverty between 1997 and 2007. The other 26 households had either never been poor or were still poor, or had progressed in their lifecycle and remaining resources were divided by fewer dependants. Thus, a number of con-clusions are drawn for the interpretation and further use of such panel data. Sec-ond, the interviews with ‘real’ poverty exiters confirm that the integration into agricultural value chains can offer a stable pathway out of poverty, if the agricul-ture and livestock portfolio of the households is productive, receives invest-ments and innovation, is commercially oriented and linked to markets. Against the common notion that specialisation in few activities usually marks this neces-sary productivity, here, a combined specialised and diversified pathway is ob-served to be most successful. Agricultural value chain development with a focus on horizontal cooperation and collective marketing of cash crops or dairy in combination with a diversified food crop portfolio seems to have been the most promising pathway out of rural poverty. Both result areas provide recommendations for the implementation of future ag-ricultural value chain projects as well as for future rural poverty research.:1 INTRODUCTION 2 POVERTY AND GROWTH DEBATES AND THEIR IMPLICATIONS FOR AID TO AGRICULTURE 3 POVERTY DYNAMICS AND POVERTY EXITS: CONCEPTS, METHODOLOGIES AND CASES STUDIES 4 EMPIRICAL EVIDENCE: POVERTY EXITS IN RURAL KENYA 5 CONCLUSIONS AND RECOMMENDATIONS

In practice, when one has many candidate variables as explanatory variables in multiple regression, there is always the possibility that variables that are important determinants of the response variable might be omitted from the model, while unimportant variables might be included. Both types of errors are important, and in this dissertation it is attempted to quantify the probabilities of these errors. A simulation study is reported in this dissertation. Different numbers of variables, i.e. p= 4 to 20 are assumed, and different sample sizes, i.e. n=0.5p, p, 2p, 4p. For each p the underlying model assumes that roughly half of the independent variables are actually correlated with the dependant variable and the other half not. The noise is ε~ N(0, σ2, where σ2, is set fixed. The data was simulated 10000 times for each combination of n and p using known underlying models and ε randomly selected from of a normal distribution. For this investigation the full model and forward selection regression are compared. The mean squared error of the estimated coefficient β(p) is determined from the true β of each n and p set. A full discussion, as well as graphs, is presented. / Dissertation (MSc)--University of Pretoria, 2011. / Statistics / unrestricted

Examples from four disciplines were used to introduce the coefficient of variation which was considered to have considerable usage and application in solving Quality Control and Reliability problems. The statistical properties were found in the statistical literature and are presented, namely, the mean and the variance of the coefficient of variation. The cumulative probability function was determined by two approximate methods and by using the noncentral t distribution. A graphical method to determine approximate confidence intervals and a method to determine if the coefficients of variation from two samples were significantly different from each other are also provided (with examples). Applications of the coefficient of variation to solving some of the main problems encountered in industry that are included in this report are: (a) using the coefficient of variation to measure relative efficiency, (b) acceptance sampling, (c) stress versus strength reliability problem, and (d) estimating the shape parameter of the two parameter Weibull. (84 pages)

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Consider a generalized multiterminal source coding system, where 􏱡(l choose m) 􏱢 encoders, each m observing a distinct size-m subset of l (l ≥ 2) zero-mean unit-variance symmetrically correlated Gaussian sources with correlation coefficient ρ, compress their observation in such a way that a joint decoder can reconstruct the sources within a prescribed mean squared error distortion based on the compressed data. The optimal rate- distortion performance of this system was previously known only for the two extreme cases m = l (the centralized case) and m = 1 (the distributed case), and except when ρ = 0, the centralized system can achieve strictly lower compression rates than the distributed system under all non-trivial distortion constaints. Somewhat surprisingly, it is established in the present thesis that the optimal rate-distortion preformance of the afore-described generalized multiterminal source coding system with m ≥ 2 coincides with that of the centralized system for all distortions when ρ ≤ 0 and for distortions below an explicit positive threshold (depending on m) when ρ > 0. Moreover, when ρ > 0, the minimum achievable rate of generalized multiterminal source coding subject to an arbitrary positive distortion constraint d is shown to be within a finite gap (depending on m and d) from its centralized counterpart in the large l limit except for possibly the critical distortion d = 1 − ρ. / Thesis / Master of Applied Science (MASc)

Consider a lossy compression system with l distributed encoders and a centralized decoder. Each encoder compresses its observed source and forwards the compressed data to the decoder for joint reconstruction of the target signals under the mean squared error distortion constraint. It is assumed that the observed sources can be expressed as the sum of the target signals and the corruptive noises, which are generated independently from two (possibly di erent) symmetric multivariate Gaussian distributions. Depending on the parameters of such Gaussian distributions, the rate-distortion limit of this lossy compression system is characterized either completely or for a subset of distortions (including, but not necessarily limited to, those su fficiently close to the minimum distortion achievable when the observed sources are directly available at the decoder). The results are further extended to the robust distributed compression setting, where the outputs of a subset of encoders may also be used to produce a non-trivial reconstruction of the corresponding target signals. In particular, we obtain in the high-resolution regime a precise characterization of the minimum achievable reconstruction distortion based on the outputs of k + 1 or more encoders when every k out of all l encoders are operated collectively in the same mode that is greedy in the sense of minimizing the distortion incurred by the reconstruction of the corresponding k target signals with respect to the average rate of these k encoders. / Thesis / Master of Applied Science (MASc)