The Allelic Abundance of Afghanistan, a Pool for West and South Eurasian Genes and a Blockade against Eastern Admixture

In this study, I divided samples from individuals within Afghanistan based upon geography (i.e., north versus south). I determined allelic frequencies and other statistical parameters for 15 STR loci (i.e., D8S1179, D21S11, D7S820, CSF1PO, D3S1358, TH01, Dl3S317, D16S539, D2S1338, D19S433, vWA, TPOX, D18S51, D5S818, and FGA). I conducted pairwise comparisons with 19 neighboring Eurasian populations to assign Gstatistics and p-values. Categorizing the populations into five groups (i.e., Central Asia, East Asia, South Asia, the Middle East, and the Caucasus/Anatolia), I derived values for intra-population, inter-population, and total variance. Admixture analyses determined the highest allelic contributions to be from the Caucasus/ Anatolia, while negligible contributions were made by Central Asia and East Asia. A Correspondence Analysis revealed clustering of both northern and southern Afghanistan with Georgia, Turkey, northern Iran, and southern Iran of the Caucasus/ Anatolia and the Middle East. A Neighbor-Joining phylogenetic tree was constructed to generate bootstrap values over 1, 000 reiterations.

An Alternative Goodness-of-fit Test for Normality with Unknown Parameters

Goodness-of-fit tests have been studied by many researchers. Among them, an alternative statistical test for uniformity was proposed by Chen and Ye (2009). The test was used by Xiong (2010) to test normality for the case that both location parameter and scale parameter of the normal distribution are known. The purpose of the present thesis is to extend the result to the case that the parameters are unknown. A table for the critical values of the test statistic is obtained using Monte Carlo simulation. The performance of the proposed test is compared with the Shapiro-Wilk test and the Kolmogorov-Smirnov test. Monte-Carlo simulation results show that proposed test performs better than the Kolmogorov-Smirnov test in many cases. The Shapiro Wilk test is still the most powerful test although in some cases the test proposed in the present research performs better.

Inferences about Parameters of Trivariate Normal Distribution with Missing Data

Multivariate normal distribution is commonly encountered in any field, a frequent issue is the missing values in practice. The purpose of this research was to estimate the parameters in three-dimensional covariance permutation-symmetric normal distribution with complete data and all possible patterns of incomplete data. In this study, MLE with missing data were derived, and the properties of the MLE as well as the sampling distributions were obtained. A Monte Carlo simulation study was used to evaluate the performance of the considered estimators for both cases when ρ was known and unknown. All results indicated that, compared to estimators in the case of omitting observations with missing data, the estimators derived in this article led to better performance. Furthermore, when ρ was unknown, using the estimate of ρ would lead to the same conclusion.