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

In a variance component model,(Formula presented.), Pukelsheim (1981) proved that the non-negative and unbiased estimation of the variance components σ(Formula presented.), j=1, …, c, entails a transformation of the original model to Q(Formula presented.) (called Q-reduced model). The maximum likelihood (ML) approach based on the likelihood of Q(Formula presented.) (denoted Q-ML) is considered and applied to an incomplete block design (IBD) model. The Q-ML estimators of variance components and are shown to be more efficient in the mean squared error sense than the non-negative MINQUE’s (minimum norm quadratic unbiased estimators) in the IBD. The effect of using Q-ML estimators of the variance components to estimate the variance ratio in the combined estimator of the treatment contrast is also considered.

No description available.

No description available.

Maximum likelihood symbol timing estimation for communication over a frequency non-selective MIMO fading channel is developed. The cases of known data (data-aided estimation) and unknown data (non-data-aided estimation) together with known channel and unknown channel are considered. The analysis shows that the log-likelihood functions and their approximations can be interpreted as SISO log-likelihood functions operating on each of the receive antennas. Previously published symbol timing estimators are shown to be special cases of the more general framework presented. Architectures based on both block processing and sequential processing using a discrete-time phase-locked loop are summarized. Performance examples over a MIMO channel based on measured data and on a simple stochastic MIMO channel model are given. These examples show that the mean-squared error performance of these techniques is not strongly dependent on the MIMO channel and is able to reach the Cramer Rao bound when sufficient complexity is applied.

The normal distribution is a commonly seen distribution in nature, education, and business. Data that are mounded or bell shaped are easily found across various fields of study. Although there is high utility with the normal distribution; often the full range can not be observed. The truncated normal distribution accounts for the inability to observe the full range and allows for inferring back to the original population. Depending on the amount of truncation, the truncated normal has several distinct shapes. A simulation study evaluating the performance of the maximum likelihood estimators and method of moment estimators is conducted and a comparison of performance is made. The α Likelihood Ratio Test (LRT) is derived for testing the null hypothesis of equal population means for truncated normal data. A simulation study evaluating the power of the LRT to detect absolute standardized differences between the two population means with small sample size was conducted and the power curves were approximated. Another simulation study evaluating the power of the LRT to detect absolute differences for testing the hypothesis with large unequal sample sizes was conducted. The α LRT was extended to a k population hypothesis test for equal population means. A simulation study examining the power of the k population LRT for detecting absolute standardized differences when one of the population means is different than the others was conducted and the power curve approximated. Stat~221 is the largest introductory statistics course at BYU serving about 4,500 students a year. Every section of Stat 221 shares common homework assignments and tests. This controls for confounding when making comparisons between sections. Historically grades have been thought to be bell shaped, but with grade inflation and other factors, the upper tail is lost because of the truncation at 100. It is reasonable to assume that grades follow a truncated normal distribution. Inference using the final grades should be done recognizing the truncation. Performance of the different Stat 221 sections was evaluated using the LRTs derived.

Segmented regression is a type of nonlinear regression that allows differing functional forms to be fit over different ranges of the explanatory variable. This paper considers the simple segmented regression case of two linear segments that are constrained to meet, often called the linear-linear model. Parameter estimation in the case where the joinpoint between the regimes is unknown can be tricky. Using a simulation study, four estimators for the parameters of the linear-linear model are evaluated. The bias and mean squared error of the estimators are considered under differing parameter combinations and sample sizes. Parameters estimated in the model are the location of the change-point, the slope and intercept of the first segment, the change in slope from the first segment to the second, and the variance over both segments.

No description available.

Heteromys pictus-spectabilis is a species complex within the subfamily Heteromyinae (Family: Heteromyidae) that is distributed along the western and southern Mexican coast and surrounding environments. Currently, the species complex is accepted as being 2 separate species (H. pictus and H. spectabilis), but this also renders H. pictus paraphyletic. Therefore, the species complex requires re-evaluation in order to resolve the paraphyly. Mitochondrial DNA sequences from a previously existing ~720 specimen database compiled by Victoria Vance were used in conjunction with new nuclear DNA sequences sequenced for the purpose of this study to generate multiple phylogenetic trees via the software programs RAxML, BEAST, and MrBayes to evaluate how different haplotype networks were related to each other. Using these molecular datasets in consideration with Kimura two-parameter values, time calibrations via BEAST, and the relative geographic locations of the haplotype networks, the results strongly indicate this species complex is composed of multiple cryptic species and potentially multiple genera. This was a preliminary exploration into this species complex however, and future research will be required to verify these findings.

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)