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The thesis deals with extreme value distributions and censored samples. Theoretical part describes a maximum likelihood method, types of censored samples and introduce a extreme value distributions. In the thesis are derived likelihood equations for censored samples from exponential, Weibull, lognormal, Gumbel and generalized extreme value distribution. For these distributions are also derived asymptotic interval estimates and is made simulation studies on the dependence of the parameter estimate on the percentage of censoring.

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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.

We propose a simple adjustment to a Wald confidence interval to estimate a linear function of binomial proportions. This method is an extension to the adjusted Wald confidence intervals for proportions and their differences that have recently been proposed.

This thesis investigates the use of Maximum Likelihood Sequence Estimation (MLSE) in the presence of unknown channel parameters. MLSE is a fundamental problem that is closely related to many modern research areas like Space-Time Coding, Overloaded Array Processing and Multi-User Detection. Per-Survivor Processing (PSP) is a technique for approximating MLSE for unknown channels by embedding channel estimation into the structure of the Viterbi Algorithm (VA). In the case of successful acquisition, the convergence rate of PSP is comparable to that of the pilot-aided RLS algorithm. However, the performance of PSP degrades when certain sequences are transmitted. In this thesis, the blind acquisition characteristics of PSP are discussed. The problematic sequences for any joint ML data and channel estimator are discussed from an analytic perspective. Based on the theory of indistinguishable sequences, modifications to conventional PSP are suggested that improve its acquisition performance significantly. The effect of tree search and list-based algorithms on PSP is also discussed. Proposed improvement techniques are compared for different channels. For higher order channels, complexity issues dominate the choice of algorithms, so PSP with state reduction techniques is considered. Typical misacquisition conditions, transients, and initialization issues are reported. / Master of Science

Chiral Perturbation Theory (ChPT) is a tool for studying the strong interaction at low energies. The Perturbation theory is developed around the limit where the light quarks, u,d,s are approximated to be massless. In this approximation the isospin symmetry, one of the main features of the strong interaction, is fulfilled automatically. The study of the light quark masses and isospin violation can be done with the η'→πππ and η'→ηππ decay channels by analyzing the kinematic distribution using so-called Dalitz plots. A Dalitz plot analysis of the η'→ηπ+π- decay mode is conducted by the BESIII collaboration. The unbinned maximum likelihood method is used to fit the parameters that describe the Dalitz plot distribution. In this fit a polynomial expansion of the matrix element squared is used. However, in order to study light quark masses, it is better to use a parameterization which includes the description of the final-state interaction based on a dispersion relation. Hence, it is desirable to use a representation of the Dalitz plot as a two-dimensional histogram with acceptance corrected data as input to extract the substraction constants. Therefore, the goal of this thesis is to make a consistency check between the unbinned and binned representation of the data. In this thesis Monte Carlo data of η'→ηπ+π- decay channel is generated based on the BESIII. An unbinned maximum likelihood fit is performed to find the Dalitz plot parameters repeating the BESIII analysis method. The Monte Carlo data is then used for a binned maximum likelihood and a χ2 fit. Finally, the prepared binned experimental acceptance corrected data from BESIII is used to fit the Dalitz plot parameters using the same statistical methods. The results based on the binned maximum likelihood and the χ2 methods are consistent with the fit using the unbinned maximum likelihood method applied in the original BESIII publication.

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