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Dissertation

It is well known that the inflation linked breakeven inflation, defined as the difference between a nominal yield and an inflation linked yield, sometimes is used as an approximation of the market’s inflation expectation. D’Amico et al. (2009, [5]) show that this is a poor approximation for the US market. Based on their work, this thesis shows that the approximation also is poor for the Swedish bond market. This is done by modelling the Swedish bond market using a five-factor latent variable model, where an inflation linked bond specific premium is introduced. Latent variables and parameters are estimated using a Kalman filter and a maximum likelihood estimation. The conclusion is drawn that the modelling was successful and that the model implied outputs gave plausible results.

If a known distribution on a real line is given, it can be wrapped on the circumference of a unit circle. This research entails the study of a univariate skew-normal distribution where the skew-normal distribution is generalised for the case of bimodality. Both the skew-normal and exible generalised skew-normal distributions are wrapped onto a unit circle, consequently referred to as a wrapped skew-normal and a wrapped exible generalised skew-normal distribution respectively. For each of these distributions a simulation study is conducted, where the performance of maximum likelihood estimation is evaluated. Skew scale mixtures of normal distributions with the wrapped version of these distributions are proposed and graphical representations are provided. These distributions are also compared in an application to wind direction data. / Dissertation (MSc)--University of Pretoria, 2019. / Statistics / MSc / Unrestricted

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The r-out-of-n F-system and load-sharing system are very common in industrial engineering. Statistical inference has been developed here for an equal-load sharing r-out-of-n F-system on Birnbaum-Sauders (BS) lifetime distribution. A simulation study is carried out with different parameter values and different censoring rates in order to examine the performance of the proposed estimation method. Moreover, to find maximum likelihood estimates numerically, three methods of finding initial values for the parameters - pseudo complete sample method, Type-II modified moment estimators of BS distribution method and stochastic approximation method - are developed. These three methods are then compared based on the number of iterations and simulation time. Two real data sets and one simulated data set are used for illustrative purposes. Finally, some concluding comments are made including possible future directions for investigation. / Thesis / Master of Science (MSc)

The alleged privacy paradox states that individuals report high values for personal privacy, while at the same time they report behavior that contradicts a high privacy value. This is a misconception. Reported privacy behaviors are explained by asymmetric subjective beliefs. Beliefs may or may not be uncertain, and non-neutral attitudes towards uncertainty are not necessary to explain behavior. This research was conducted in three related parts. Part one presents an experiment in individual decision making under uncertainty. Ellsberg's canonical two-color choice problem was used to estimate attitudes towards uncertainty. Subjects believed bets on the color ball drawn from Ellsberg's ambiguous urn were equally likely to pay. Estimated attitudes towards uncertainty were insignificant. Subjective expected utility explained subjects' choices better than uncertainty aversion and the uncertain priors model. A second treatment tested Vernon Smith's conjecture that preferences in Ellsberg's problem would be unchanged when the ambiguous lottery is replaced by a compound objective lottery. The use of an objective compound lottery to induce uncertainty did not affect subjects' choices. The second part of this dissertation extended the concept of uncertainty to commodities where quality and accuracy of a quality report were potentially ambiguous. The uncertain priors model is naturally extended to allow for potentially different attitudes towards these two sources of uncertainty, quality and accuracy. As they relate to privacy, quality and accuracy of a quality report are seen as metaphors for online security and consumer trust in e-commerce, respectively. The results of parametric structural tests were mixed. Subjects made choices consistent with neutral attitudes towards uncertainty in both the quality and accuracy domains. However, allowing for uncertainty aversion in the quality domain and not the accuracy domain outperformed the alternative which only allowed for uncertainty aversion in the accuracy domain. Finally, part three integrated a public-goods game and punishment opportunities with the Becker-DeGroot-Marschak mechanism to elicit privacy values, replicating previously reported privacy behaviors. The procedures developed elicited punishment (consequence) beliefs and information confidentiality beliefs in the context of individual privacy decisions. Three contributions are made to the literature. First, by using cash rewards as a mechanism to map actions to consequences, the study eliminated hypothetical bias as a confounding behavioral factor which is pervasive in the privacy literature. Econometric results support the 'privacy paradox' at levels greater than 10 percent. Second, the roles of asymmetric beliefs and attitudes towards uncertainty were identified using parametric structural likelihood methods. Subjects were, in general, uncertainty neutral and believed 'bad' events were more likely to occur when their private information was not confidential. A third contribution is a partial test to determine which uncertain process, loss of privacy or the resolution of consequences, is of primary importance to individual decision-makers. Choices were consistent with uncertainty neutral preferences in both the privacy and consequences domains.

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