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.

An Assessment of the Performances of Several Univariate Tests of Normality

The importance of checking the normality assumption in most statistical procedures especially parametric tests cannot be over emphasized as the validity of the inferences drawn from such procedures usually depend on the validity of this assumption. Numerous methods have been proposed by different authors over the years, some popular and frequently used, others, not so much. This study addresses the performance of eighteen of the available tests for different sample sizes, significance levels, and for a number of symmetric and asymmetric distributions by conducting a Monte-Carlo simulation. The results showed that considerable power is not achieved for symmetric distributions when sample size is less than one hundred and for such distributions, the kurtosis test is most powerful provided the distribution is leptokurtic or platykurtic. The Shapiro-Wilk test remains the most powerful test for asymmetric distributions. We conclude that different tests are suitable under different characteristics of alternative distributions.

Recent Changes in Central and Eastern Pacific El Niño

Recent research indicates that characteristics of El Niño and the Southern Oscillation (ENSO) have changed over the past several decades. Here, I examined different flavors of El Niño in the observational record and the recent changes in the character of El Niño events. The fundamental physical processes that drive ENSO were described and the Eastern Pacific (EP) and Central Pacific (CP) types or flavors of El Niño were defined. Using metrics from the peer-reviewed literature, I examined several historical data sets to interpret El Niño behavior from 1950-2010. A Monte Carlo Simulation was then applied to output from coupled model simulations to test the statistical significance of recent observations surrounding EP and CP El Niño. Results suggested that EP and CP El Niño had been occurring in a similar fashion over the past 60 years with natural variability, but no significant increase in CP El Niño behavior.