Critical values are laboratory values that represent a life-threatening condition for which there is a treatment available. Laboratories make immediate notifications to ordering providers when critical values are identified so that they may quickly act to initiate a treatment for their patient. The majority of laboratories apply the inpatient critical value list to the outpatient setting, although there are many differences between an acutely ill inpatient population and an ambulatory outpatient population. The goal of this study was to determine if providers responded to the critical values in the outpatient setting and to determine if there was a difference in outcome indicators when providers responded to notifications and when they did not respond to notifications. Data for 673 critical value notifications for PT/INR, Digoxin, and Glucose results were collected from Riverside Health System’s five laboratories. Analysis suggested that the inpatient critical value lists and thresholds may not be appropriate to apply to the outpatient setting. In this study of 637 critical value notifications, providers chose not to respond to 25.7% of critical value notifications. Providers were more likely to respond to PT/INR and Digoxin critical value notifications that glucose critical value notifications. None of the cases for either of the three tests that went without a provider response resulted in death or serious harm to a patient, indicating that the critical value thresholds do not meet the definition of a critical value in the outpatient setting. In the future, laboratories should explore the utilization of a different critical value list and thresholds for the outpatient setting based upon patient outcomes.

The purpose of this thesis is to evaluate five different volatility forecasting models that are used to calculate financial market risk. The models are used on both daily exchange rates and high-frequency intraday data from four different series. The results show that time series models fitted to high-frequency intraday data together with a critical value taken from the empirical distribution displayed the best forecasts overall.

Natural and manmade disasters have brought urban search and rescue (USAR) robots to the technology forefront as a means of providing additional support for search and rescue workers. The loss of life among victims and rescue workers necessitates the need for a wider acceptance of this assistive technology. Disasters, such as hurricane Harvey in 2017, hurricane Sandy in 2012, the 2012 United States tornadoes that devastated 17 states, the 2011 Australian floods, the 2011 Japan and 2010 Haiti earthquakes, the 2010 West Virginia coal mine explosions, the 2009 Typhoon caused mudslides in Taiwan, the 2001 Collapse of the World Trade Center, the 2005 Hurricane Katrina, the 1995 Oklahoma City bombing, and the 1995 Kobe Japan earthquake all benefited from the use of USAR. While there has been a push for use of USAR for disaster, user resistance to such technology is still significantly understudied. This study applied a mixed quantitative and qualitative approach to identify important system characteristics and critical value factors (CVFs) that contribute to team members’ resistance to use such technology. The populations for this study included 2,500 USAR team members from the Houston Professional Fire Fighters Association (HPFFA), and the expected sample size of approximately 250 respondents. The main goal of this quantitative study was to examine system characteristics and CVFs that contribute to USAR team members’ resistance to use such technology. System characteristics and CVFs are associated with USAR. Furthermore, the study utilized multivariate linear regression (MLR) and multivariate analysis of covariance (ANCOVA) to determine if, and to what extent, CVFs and computer self-efficacy (CSE) interact to influence USAR team members’ resistance to use such technology. This quantitative study will test for significant differences on CVF’s, CSE, and resistance to use such technology based on age, gender, prior experience with USAR events, years of USAR experience, and organizational role. The contribution of this study was to reduce USAR team members’ resistance to use such technology in an effort minimize risk to USAR team members while maintaining their lifesaving capability.

The purpose of this research is to develop a statistical method to monitor the fairness of network resource distribution. The newly developed fairness score function allows users to have the same or different priority levels. Especially, this function possesses all the necessary properties required as a quality characteristic for the purpose of statistical process control. The main objective is to find the critical values for the statistical test. Monte Carlo simulation is used to find the critical values. When the users have the same priority level, a table of the critical values is given for different sample sizes and different significance levels. When the users have different priority levels, it is difficult to generate a similar table since the users’ priority levels vary. Therefore, the critical values are computed for given priority levels. In both cases, an example is given to demonstrate the approach developed in this study.

The emphasis of this diploma thesis is placed on the verification of stationarity in time series using the Unit Root Tests and their most common modifications that are introduced in the theoretical part of this paper. Tests mainly by Dickey and Fuller, Phillips and Perron, and KPSS test are introduced as well as their modifications in the form of ERS, Ng and Perron, and Leybourne and McCabe tests. Moreover the HEGY test for testing stationarity in the seasonal Time series and Perron test of structural breaks for Time series with shocks are described. There is also outlined the process of testing multiple Unit Roots. The empirical part of this paper consists of simulations of AR(1) time series generated using the software R, their testing for stationarity by selected Unit Root tests and the comparison of power of these tests. The conclusion includes recommendations which tests and under what conditions are the most suitable for testing Time series for the presence of Unit Root.

Η παρούσα διατριβή εκπονήθηκε με σκοπό να γενικεύσει το πρόβλημα του ελέγχου υποθέσεων που εμπεριέχουν στοχαστική διάταξη στα πλαίσια της Μη Παραμετρικής Στατιστικής. Για τον σκοπό αυτό μελετήθηκε η σχετική βιβλιογραφία, εξετάσθηκε η ορολογία, οι ήδη υπάρχοντες ορισμοί και οι σχετικές προταθείσες μέθοδοι και ακολούθως έγινε προσπάθεια γενίκευσης του προαναφερθέντος προβλήματος. Η έρευνα αυτή απέδωσε δύο ομάδες αποτελεσμάτων. Στην πρώτη, ορίσθηκε μια νέα ολική διάταξη (XFO) σε κάθε σύνολο ασαφών αριθμών που έχουν διαφορετικές κορυφές οι οποίες σχηματίζουν συμπαγές υποσύνολο του ℝ. Η ασαφής αυτή διάταξη αποδίδει την σύγκριση των ασαφών αριθμών με ένα ασαφές μέτρο αναγκαιότητας και με το δυϊκό του μέτρο δυνατότητας. Η σύγκριση αυτής της μεθόδου με την πλέον αναγνωρισμένη αντίστοιχη μέθοδο διάταξης ασαφών αριθμών απέδειξε ότι η εισαχθείσα μέθοδος XFO είναι πιο κοντά στην αρχική μας εκτίμηση για την διάταξη και ανταποκρίνεται πιο αισιόδοξα. Στην δεύτερη ομάδα αποτελεσμάτων εισάγεται η έννοια της στοχαστικής διάταξης ασαφών τυχαίων μεταβλητών, με σύντηξη των ακολούθων εννοιών: α) της στοχαστικής διάταξης, β) της ανωτέρω ασαφούς διάταξης και γ) της εισαγόμενης έννοιας της ασαφούς συνάρτησης κατανομής. Ο ορισμός της στοχαστικής διάταξης δίδεται σε αρμονία με την μέθοδο XFO, αφού και οι δύο έχουν τις ρίζες τους στην ίδια διάταξη κλειστών διαστημάτων που εισάγεται αρχικά στην εργασία, μπορεί δε να θεωρηθεί η ασαφής στοχαστική διάταξη ως επέκταση της XFO. Η δεύτερη αυτή ομάδα περιλαμβάνει ένα εισαγόμενο για πρώτη φορά τρόπο ορισμού Ασαφών Υποθέσεων που περιέχουν στοχαστική διάταξη ασαφών τυχαίων μεταβλητών. Αυτό έχει αποτέλεσμα να βαθμολογείται θετικά μόνο η μία εκ των δύο ασαφών υποθέσεων, ασαφούς μηδενικής και ασαφούς εναλλακτικής, διευκολύνοντας έτσι την λήψη αποφάσεων. Προτείνεται διαδικασία ασαφούς ελέγχου που πιστοποιεί οποιαδήποτε ενυπάρχουσα στοχαστική διάταξη δύο ασαφών τυχαίων δειγμάτων, συμβατή με τον ορισμό, η οποία αντιστοιχεί θετικές τιμές αλήθειας μόνον στην αποδεκτή υπόθεση και μηδέν στην απορριπτόμενη. Τα αποτελέσματα του ελέγχου εκφράζονται με την βοήθεια δύο μέτρων αναγκαιότητας. Η μείζων συνεισφορά της προτεινόμενης ασαφούς διαδικασίας ελέγχου ασαφών υποθέσεων, που αναφέρονται σε στοχαστική διάταξη ασαφών τυχαίων μεταβλητών, είναι ότι παρέχει εργαλείο μετασχηματισμού του προβλήματος σε ένα περιορισμένο αριθμό ελέγχων κλασσικών υποθέσεων της μη Παραμετρικής Στατιστικής. Με τον τρόπο αυτό μπορούμε να συμβάλουμε στην επίλυση τέτοιων προβλημάτων ασαφών ελέγχων τόσο θεωρητικών ζητημάτων στοχαστικής διάταξης ασαφών τυχαίων μεταβλητών όσο και ενός αριθμού πρακτικών προβλημάτων, όπως της ασαφούς αξιολόγησης εξεταζομένων. / This dissertation has been carried out in order to extend the problem of testing hypotheses on stochastic orderings, with methods based on ranks. This study provides two sets of related results. In the first set of results we introduce a novel linear order, the “extended fuzzy order” (XFO), on every subset of F(ℝ), the members of which must have their modal values all different and form a compact subset of ℝ. A distinct new feature is that our linear determined procedure employs the corresponding order of a class interval associated with a confidence measure which assigns a necessity measure value on every comparison . This new XFO method measures the ordering of any two fuzzy numbers with a possibility and a necessity measure, a feature that makes the method relevant for processing of fuzzy statistical data. These fuzzy measures are compared with the widely accepted PD and NSD indices of D. Dubois and H. Prade. The comparison proves that our possibility and necessity measures are more optimistic and comply better with our intuition. In the second set of results it is investigated the fuzzy extension of hypotheses testing using non parametric methods based on ranks. To achieve this, the notion of fuzzy distribution function is introduced in a practical manner, which is proved to be equivalent to the known notion of Kruse and Mayer. The stochastic ordering of two fuzzy random samples is defined in a fusion of the notion of stochastic ordering, fuzzy distribution function and XFO method. A novel definition of fuzzy hypotheses related to a potential fuzzy stochastic order between two fuzzy random samples is given in a new manner so that the null and its alternative hypotheses do not overlap. Consequently, the method assigns positive possibility grades either to the null fuzzy hypothesis or to the its fuzzy alternative. This simplifies the fuzzy decision making, and moreover there is no need to defuzzify the results if a clear cut decision is required. A fuzzy statistical inference procedure of fuzzy hypotheses is proposed and it is carried out at a fuzzy significance level. The definition of a fuzzy critical value is required, which is carried out in a practical manner. The proposed method certifies any underlying stochastic fuzzy order between two fuzzy random samples giving grades of confidence to that. Two necessity measures are assigned to the rejection of the fuzzy null hypothesis in favor of its alternative. The first measures the necessity of the existence of any fuzzy stochastic ordering between the fuzzy random samples under examination. The second necessity measure expresses the confidence of the fuzzy null hypothesis rejection uniformly for all relevant α-cut levels. The main contribution of this thesis, as far as the second set of results is concerned, is that a problem of testing fuzzy hypotheses on stochastic orderings of fuzzy random variables at a fuzzy significance level, is transferred to a limited number of tests of classic hypotheses. These tests are carried out at a fuzzy significance level, and are processed with the application of the linear fuzzy ordering procedure XFO.

In this paper, we will investigate the important properties of three major parts of statistical inference: point estimation, interval estimation and hypothesis testing. For point estimation, we consider the two methods of finding estimators: moment estimators and maximum likelihood estimators, and three methods of evaluating estimators: mean squared error, best unbiased estimators and sufficiency and unbiasedness. For interval estimation, we consider the the general confidence interval, confidence interval in one sample, confidence interval in two samples, sample sizes and finite population correction factors. In hypothesis testing, we consider the theory of testing of hypotheses, testing in one sample, testing in two samples, and the three methods of finding tests: uniformly most powerful test, likelihood ratio test and goodness of fit test. Many examples are used to illustrate their applications.