Probability plots and order statistics of the standard extreme value distribution

A comparison between the ordinary least-squares estimator and the weighted least-squares estimator when the data set arises from the standard extreme value distribution is provided. Probability plot of the extreme value distribution is applied. A goodness-of-fit test of the standard extreme value distribution is introduced. The percentage points of the test statistic are investigated. The results of power study for the test statistic under various alternatives show that in most situations the proposed test statistic serves as well as do competing alternatives

Some Contributions to Description and Validation of the Extreme Value Distribution

This thesis focuses on the validation and description of the Gumbel distribution. Since this is a scale and location parameter distribution, the generalized least squares regression of the order statistics on the expected values can be used, without the necessity of iteration, to obtain the best linear unbiased estimates of the parameters. In order to implement this procedure, we need information about the expected values and variances-covariances of order statistics from the standard extreme value distribution. Numerical problems in determining these values and lack of exact values of means, variances for n > 100 and covariances for n > 30, are major challenges which we must deal with. In two papers, by applying the method of least squares, we present approximation algorithms to approximate the means, variances and covariances of the order statistics of the standard extreme value distribution. In both papers we compare the accuracy of our proposed models by using available tabulated values and values obtained from Monte Carlo methods. In the case where one or both of the parameters in the distribution are known or unknown, as in papers three to six, we present and compare goodness-of-fit tests based on different approaches. These papers tackle tests of the null hypothesis that a random sample comes from the extreme value distribution of type I (minima). The test procedure is to calculate an appropriate test statistic and reject null hypothesis if the value of the statistic used exceeds the percentage point at the type I error level

First moment approximations for order statistics from the extreme value distribution

Approximate expressions of the first moment of the order statistics of standard extreme value distributions are proposed. We compare different previously given approximations with the exact values. The results show that the approximation given here fits the exact values better than previously given models

Approximations of variances and covariances for order statistics from the standard extreme value distribution

We consider simple approximations of variances and covariances for order statistics from the standard extreme value distribution. Exact values and simulation results of the variances and covariances for certain sample sizes are used to determine the validity of the suggested approximations

Trust in the healthcare system and mortality : A population-based prospective cohort study in southern Sweden

Aims: To investigate associations between trust in the healthcare system and all-cause, cardiovascular, cancer and other causes mortality. Study design: Prospective cohort study. Methods: A public health questionnaire was conducted in 2008 in Scania, the southernmost part of Sweden, with a 54.1% participation rate with a postal questionnaire and three reminders. In this study 24,833 respondents were included. The baseline questionnaire study was linked to prospective 8.3-year follow-up cause-specific mortality register data. Survival (Cox) regression analyses were conducted. Results: A 15.2% proportion of respondents reported very high, 59.1% rather high, and 21.7% not particularly high trust in the healthcare system, while 3.2% reported no trust at all and 0.9% did not know. The groups with rather high and not particularly high trust in the healthcare system had significantly lower all-cause mortality than the reference group with very high trust in the healthcare system. These statistically significant results remained throughout the multiple analyses, and were explained by lower cancer mortality in both the rather high and not particularly high trust respondent groups, and lower cardiovascular mortality in the not particularly high trust respondent group. No significant results were observed in the adjusted models for other causes mortality. No significant results were observed for the no trust and don't know categories in the multiple adjusted models, but these groups are small. Conclusions: The results suggest a comparative advantage of moderate trust compared to very high trust in this setting of long waiting times for cancer and CVD treatment