Statistical distributions also known as probability distributions are used to model a random experiment. Probability distributions consist of probability density functions (pdf) and cumulative density functions (cdf). Probability distributions are widely used in the area of engineering, actuarial science, computer science, biological science, physics, and other applicable areas of study. Statistics are used to draw conclusions about the population through probability models. Sample statistics such as the minimum, first quartile, median, third quartile, and maximum, referred to as the five-number summary, are examples of order statistics. The minimum and maximum observations are important in extreme value theory. This paper will focus on the probability distribution of the minimum observation, also known as the first order statistic, when the sample size is random.

Adolescent obesity is an area of growing public health concern. The Centers for Disease Control and Prevention conducts surveys through their Youth Risk Behavior Surveillance System (YRBSS) every two years to monitor a variety of health risk factors and behaviors among high school and middle school students. The YRBSS compiles information about obesity and BMI percentile, among many other factors. We accessed a combined dataset available on the YRBSS website which includes all data collected from high school students’ surveys from 1991 to 2013. Due to updating of questionnaires and adding of variables over the years, some variables only appear in the most recent years, limiting trend analysis to the timeframe in which the variable of interest was included. We analyzed the linear and quadratic trends in BMI percentile, obesity, and overweight rates in the national Youth Risk Behavior Survey (YRBS) from 1999 to 2013 and in the Tennessee YRBS from 2003 to 2013. Each variable was stratified by age and race to observe differences among groups. National trends show an increase in average BMI percentiles overall from 1999 to 2007, a decrease between 2007 and 2009, then another increase between 2009 and 2013. Tennessee trends show a dramatic increase in average BMI percentile overall from 2003 to 2007, then a decrease between 2007 and 2013. Since 2005, Tennessee has maintained a higher average BMI percentile (64.23, 66.37, 65.00, 64.96, 64.23) than the national average (63.47, 64.23, 62.81, 63.00, 63.51) for each recorded year, however, the decreasing trends in Tennessee and increasing trends in the nation have brought the average BMI percentiles of each to comparable rates. There is literature to support the variation of BMI among young, middle-aged, and elderly individuals. However, there is currently little evidence of differences in BMI percentiles, obesity, or overweight rates between different age groups of high school students. We expect to see little, if any, differences across different age groups of high school students in this study both nationally and at the state level. Racial and ethnic disparities exist for a variety of health conditions and outcomes. Many conditions, including obesity, disproportionately affect minority populations. We expect to see differences in BMI percentiles, obesity, and overweight rates across different races at both nationally and at the state level.

This study evaluates the accuracy of approach volumes and free flow approach speeds collected by the Wavetronix SmartSensor Advance sensor using the field data collected by JAMAR counter boards for free flow approach volumes and a TruCam LiDAR gun for approach speeds. The Advance sensor is primarily designed for dilemma zone reduction. It does not have the capability to differentiate between lanes, but the Advance sensor currently used has a detection range of up to 600 ft. and has the capability to track vehicles approaching the intersection. The Utah Department of Transportation (UDOT) wanted to use this capability to get added values from their investment in the Advance sensors. The approach volume accuracy was analyzed with three factors: sensor position, number of approach lanes, and approach volume level. The results showed that the high accuracy is achieved when the number of approach lanes is low, or closer to one-lane, and the approach volume level is low. It was found that the accuracy of the approach volume counts was not affected by the sensor position. As a result of the sensor's inability to differentiate lanes, the more cars travel alongside each other, the more likely they are to be detected together as one vehicle. The overall range of accuracy for the approach volume counts was found to range from approximately 76% (24% undercount) to 106% (6% overcount). The accuracy of approach speeds was analyzed with two factors: the number of lanes and offset position of the lanes relative to the location of the speed gun. First, the lane position and offset were tested to see if any effect exists on the difference between the measurements of the speed by the LiDAR gun and the Advance sensor. Then the difference between mean speeds was tested. Each site was analyzed individually and there were some sites which had a statistically significant difference while there were others which did not. However, the difference was considered not to be practically significant because of the difference in mean speeds of the sample being approximately ±2 mph. The speeds were also used to calculate the 85th percentile speed for all sites with more than 50 samples. For these sites, the average difference in 85th percentile speed was -0.43 mph, the biggest negative difference was -1.6 mph, and the biggest positive difference was 1.5 mph. Because of the limited number of samples taken at each site, a statistical resampling method called Bootstrapping was performed to predict the expected distribution of speed differences in 85th percentile speeds. The results of this analysis also showed the 85th percentile speeds by the LiDAR gun and the Advance sensor were not significantly different for practical traffic engineering applications. However, it is recommended that more research be performed to better understand the applicability of 85th percentile speed measurements.

Außerhalb ihrer ursprünglichen Heimat in Südamerika steigt die Anzahl der Alpakas stetig an. Die Tiere erfreuen sich auch in Deutschland einer großen Beliebtheit. Aktuellen Schätzungen zufolge leben in Deutschland circa 10.000 Alpakas. Siewerden zur Wollgewinnung, sowie als Begleit- und Therapietiere in kleinen Hobbyhaltungen oder in Beständen mit einer Herdengröße von bis zu 150 Tieren gehalten. Damit verbunden werden auch zunehmende Ansprüche an die Qualität der tierärztlichen Betreuung dieser Neuweltkameliden gestellt. Die Beurteilung des Wachstums und der Entwicklung junger Alpakas bildet dabei, genauso wie im Rahmen der Zucht, eine wichtige Grundlage. Derzeit existieren nur unzureichende Informationen über den Wachstumsverlauf beim Alpaka. Bisher dienten proportional angepasste Daten vom Lama zur Orientierung. Das Ziel dieser Arbeit ist die auf morphometrischen Daten basierende Beschreibung der physiologischen Entwicklung des Skelettes und des Körpergewichtes beim Alpaka in den ersten 36 Lebensmonaten. Weiterhin soll untersucht werden, welche Faktoren Einfluss auf das Wachstum junger Alpakas haben. Die Bestimmung einer Gleichung zur Berechnung des Körpergewichtes stellt einen weiteren Schwerpunkt der Arbeit dar. Über einen Zeitraum von 12 Monaten wurden 162 Alpakas im Alter von wenigen Tagen bis zu 36 Monaten vermessen. In einem zweiwöchentlichen Rhythmus wurden 9 verschiedene Parameter bei jedem Tier erfasst: Gewicht, Widerristhöhe, Hüfthöhe, Rückenlänge, Rumpflänge, Tuberculum majus-Olecranon-Distanz (TOD), Basis patellae-Tuber ischiadicum-Distanz (BTD), Thoraxumfang und Body Condition Score. Mit Hilfe von speziell angefertigten Messschiebern, einer digitalen Waage und einem flexiblen Maßband erfolgte die Datenerhebung am stehenden Tier. Das Wachstum beeinflussende Faktoren wurden mittels Allgemeiner Untersuchung der Tiere, stichprobenartigen Kotprobenuntersuchungen, Futtermittelanalysen und vom Halter ausgefüllten Fragebögen erfasst. Die erhobenen Messwerte wurden unter Verwendung der nichtparametrischen Regression LOESS (locally weighted scatterplot smoothing) zur Erstellung von Wachstumskurven genutzt, die den durchschnittlichen Wachstumsverlauf des Körpergewichtes, sowie verschiedener Körpermaße von bis zu 36 Monate alten Alpakas darstellen. Sie ermöglichen die Beurteilung der körperlichen Entwicklung eines Alpakas. Unter Anwendung der LMS-Methode (Schiefe der Verteilung der Messwerte λ [L], Mittelwert M, Standardabweichung S) wurden Perzentilkurven von vier Parametern erstellt, die als Referenzkurven und Richtlinien zur Beurteilung der tierartspezifischen Größe und des Gewichtes genutzt werden können. Wachstumsprognosen und Rückschlüsse auf das Alter eines Alpakas sind mit Hilfe der Perzentilkurven möglich. Sowohl die Wachstumskurven als auch die Perzentilkurven lassen erkennen, dass Alpakas mit 36 Monaten noch nicht ausgewachsen sind. Die Kurven wurden anhand von Messwerten von Alpakas erarbeitet, die unter Bedingungen gehalten wurden, die keinen beziehungsweise einen minimalen Einfluss auf das Wachstum haben. Dies ist anhand der Ergebnisse der parasitologischen Untersuchungen und der Futtermittelanalysen erkennbar. Weitere Auswertungen der Messdaten zeigen, dass keine signifikanten Entwicklungsunterschiede zwischen Hengsten und Stuten beziehungsweise zwischen der Rasse Huacaya und der Rasse Suri bestehen. Ähnlich wie bei anderen Tierarten auch, eignet sich der Thoraxumfang zur zuverlässigen Berechnung des Körpergewichtes besonders gut. Eine große Korrelation besteht auch zwischen der Rumpf- beziehungsweise der Rückenlänge und dem Körpergewicht. Praktische Bedeutung haben die Erkenntnisse dieser Arbeit vor allem für Alpakazüchter und –halter, sowie für Veterinärmediziner. Die Ergebnisse bilden eine wichtige Grundlage für das Fütterungs- und Reproduktionsmanagement beim Alpaka. / The number of alpacas bred outside their natural habitat in South America increases continuously. Alpacas become more and more popular in Germany. According to recent estimates about 10.000 alpacas live in Germany. They are used for wool production, as companion animal and for therapeutic treatments. The alpacas are kept as pets in smaller groups or as livestock in herds of up to 150 animals. Due to the rising number of these camelids in Germany and more intense use, higher demands on the quality of veterinary care of alpacas occur. Knowledge and data on growth and development in young alpacas are essential for an objective health evaluation as well as for breeding management. Currently very limited information is available on growth of alpacas and the data published have been adapted by calculation using measurements performed on llamas. The primary objective of this study was to determine the physiological development of the skeleton and the body weight of alpacas from birth until 36 months of age based on morphometric data. An additional aim was to analyze factors that influence the growth of young alpacas. A third focus of this study was to generate a mathematical formula to calculate the body weight. The measurements were performed on 162 alpacas with an age ranging from the first day of life up to 36 months. For each alpaca nine different parameters were determined every two weeks: body weight, height at withers, height in the hip, thoracic circumference, length of the back, length of the trunk, Greater tubercle-Olecranon-distance (TOD), Base of the patella-Ischial tuber-distance (BTD) and body condition score. All measurements were carried out on standing animals. Three custom designed caliper gauges, a digital balance and a flexible measuring tape were used to obtain the nine parameters. Factors that influence growth were captured by clinical examination, randomized fecal samples, analysis of forage and a questionnaire completed by the breeder. Based on the data collected growth curves were developed using the nonparametric regression LOESS (locally weighted scatterplot smoothing). These curves represent the average growth pattern of body weight and various body measurements of up to 36 months old alpacas. Using theses curves the physical development of this species can be assessed. By applying the LMS-Method (skewness of the measurement distribution λ [L], mean M, coefficient of variation S) percentile curves of four different parameters have been generated. They can serve as reference curves and as guidelines for objective evaluation of species specific size and weight. Using the percentile curves a reliable prediction of growth or conclusions regarding the age of an alpaca are possible. The growth curves as well as the percentile curves show that alpacas are not mature at the age of 36 months. The curves are based upon data from alpacas who were raised under environmental conditions which have no or minimized influence on growth. This is evident in the results of the parasitological examinations and the feed analysis. Further analyses indicate that no significant differences in growth exist between males and females respectively between the two breeds Huacaya and Suri. Like in other species the thoracic circumference is particularly suitable for estimating the body weight. A strong correlation exists between body weight and the length of the trunk as well as the length of the back. The results of this study are of practical significance for alpaca owners, breeders and veterinarians. They provide a sound basis for recommendations in feeding and management of reproduction.

We first consider confidence intervals for a normal percentile, an exponential percentile and a uniform percentile. Then we develop confidence intervals for a difference of percentiles from two independent normal populations, two independent exponential populations and two independent uniform populations. In our study, we mainly focus on the maximum likelihood to develop our confidence intervals. The efficiency of this method is examined via coverage rates obtained in a simulation study done with the statistical software R.

Data were collected from 60 parents of children 5-11 years of age to describe the parental and family factors and explore the associations of these factors with children's Body Mass Index (BMI) percentiles. Mother's made up 81.7% of the sample. Whites/Caucasians comprised 88.3% of the sample. Males comprised 51.6% of the child participants while females comprised 48.3%. Among the child participants, 38.3% had BMI equal to or greater than the 95th percentile, and 6.7% had BMI 85th to less than 95th percentile. Concerns about child weight (rs = 0.582), pressure to eat (rs = -0.433), and monitoring (rs = 0.348) were found to be significantly associated with children's BMI percentile. There are variations in influence of parenting and home environments on children's eating and physical activity, and in the eating and physical activity habits amongst families. Consideration of parental and family factors is needed in developing child obesity prevention programs.

There is a need for objective methods for wrist angular velocity measurements for accurate risk assessments because there is a high frequency of musculoskeletal disorder in workers. The goal of this project was to validate the accuracy of inertial measurement unit sensors to measure the angular velocity. More specifically, the purpose of this master thesis project was to apply an alternative algorithm to compute the markers velocity, other than the one from the optical system that Jenny Wingqvist, and Josephine Lantz used. The project used an experimental data of 10 participants from the previous project done by Jenny Wingqvist and Josephine Lantz. To validate the accuracy, the data of angular velocity of the sensors was compared with the data of angular velocity of markers. The lowest mean value of the root mean square differences value was 23.5 degrees/s during flexion and deviation standard movements at 40 BPM (Beats Per Minute) and the maximum value was 110.5 degrees/s at 140 BPM. The mean value of the correlation coefficients between markers and sensors angular velocities in standard movements of flexion and deviation were 0.85, 0.88, and 0.89 at 40 BPM, 90 BPM, and 140 BPM, respectively. The smallest and the largest mean value of the absolute difference in 50th percentile was found in 40 BPM (19.4±11.3), and 140 BPM (51.2±28.5) respectively. The decorrelation coefficient between the subjects 50th percentile of the angular velocity was 0.91 for the standard movements. The upper limit of agreement for the standard movements was 78.36 degrees/s, while the lower limit of agreement was -13.76 degrees/s.  The results show that the error was too large, so there is a need of further research to measure the wrist angular velocity using IMU sensors.

Objectifs : Évaluer l’incidence de la macrosomie fœtale en fonction des différentes définitions (poids de naissance >4000g, >4500g, ≥90ième percentile de Kramer) en vigueur et comparer la prévalence de la morbidité maternelle et périnatale associée à la macrosomie entre les populations Cris et les populations du Québec. Des courbes postnatales spécifiques aux Cris de l’Est de la Baie-James seront proposées. Devis : Comparaison de deux cohortes prospectives Cris et Québec. La cohorte des populations Cris de l’Est de la Baie-James, comporte 2546 femmes recrutées de 2000-2010, au cours de l’étude sur la macrosomie fœtale chez les Cris de l’Est de la Baie James. La cohorte du Québec est composée de 97475 femmes et provient de l’essai clinique randomisé multicentrique QUARISMA, 2008-2010, cette étude promulguant la réduction du taux d’accouchement par  césarienne. Méthodes : Les risques de macrosomie fœtale et de la morbidité maternelle et périnatale sont évalués par des modèles de régression logistique d’équations d'estimation généralisées (EEG) ajustés et comparés selon l’ethnicité, Cris et Québec. GEE. Le groupe de référence étant les femmes du Québec. Les courbes de croissance spécifiques aux Cris sont construites par régression quantile. Résultats : Plus du tiers, soit 36,76%, des Cris et 9,329% des nouveau-nés du Québec, ont un poids de naissance >4000g. Les résultats attestent montrent que 10,92% des Cris de l’Est de la Baie-James ont un poids de naissance de plus de 4500g, ce taux est de 1,23% au Québec. La définition de la macrosomie fœtale, par un poids néonatal ≥90ième percentile de Kramer, identifie 40,02% des bébés Cris, pour 8,83% des nourrissons du  Québec, comme macrosomes. Les Cris sont plus à risque de macrosomie fœtale, comparativement à la population générale du Québec, ces associations sont statistiquement significatives : RC=5,22; 95% IC (4,66-6,05,98), pour un poids de naissance >4000g, RC=8,10; 95% IC (6,22-10,77), pour un poids de naissance >4500g et RC=6,22; 95% IC (5,77-6,72), pour un poids de naissance ≥90ième percentile de Kramer. Le risque de la morbidité périnatale majeure, de la macrosomie fœtale, est généralement moins important pour les Cris que pour la population générale du Québec : 0,76; 95% IC 0,62-0,94. La macrosomie fœtale devrait être décrite par un poids de naissance≥95ième percentile de Kramer, pour les Cris, mais préférablement au 90ième percentile des courbes postnatales spécifiques aux Cris de l’Est de la Baie-James. Les poids de naissance diagnostique spécifiques aux Cris de l’Est de la Baie-James, au 90ième percentile de la 40ième semaine d’aménorrhée, sont de 4 417g pour les filles et 4 488g pour les garçons. Conclusions : Les courbes de Kramer diagnostiquent systématiquement plus de macrosomes chez les Cris que dans la population du Québec. Par contre, le risque de morbidité périnatale majeure est inférieur pour ces communautés autochtones, aux différents seuils décrivant la macrosomie fœtale, ce qui suggère l’utilisation de courbes spécifiques aux Cris et permettrait de diminuer les interventions obstétricales non nécessaires chez les gros bébés Cris, donc non-macrosomes. / Objective: Assess the impact of fetal macrosomia based on definitions (birth weight> 4000 g,> 4500g, ≥90ième percentile Kramer) currently used in Quebec and compare the prevalence of maternal and perinatal morbidity associated with macrosomia between the Cree populations of Eastern James Bay and the general population of Quebec. Specific postnatal curves for the Cree will be constructed. Design: Comparison of two prospective cohort Cree and Quebec. Cohort of Cree populations of eastern James Bay, has recruited 2546 women from 2000 to 2010, during the study of fetal macrosomia in the Cree of eastern James Bay. Quebec cohort consisted of 97,475 women and comes from the multicenter randomized clinical trial QUARISMA 2008-2010, this study promulgates the reduction of caesarean delivery rate. Methods: The risk of fetal macrosomia, maternal and perinatal morbidity, by ethnicity, Cree and Quebec, are evaluated by generalized estimating equations models (GEE). GEE models were adjusted to control for potentially confounding factors. The reference group is Quebec women. The specific growth curves of the Cree are built by quantile regression. Results: More than a third, 36.8%, of Cree populations of Eastern James Bay and 9.3% of newborns in Quebec have a birth weight> 4000g. For a birth weight> 4500g, the results show that 10.9% of the Cree, have a birth weight of more than 4500g, the rate is 1.2% in Quebec. The definition of fetal macrosomia by neonatal birth weight≥90th percentile of Kramer identifies 40.02% Cree’s for 8.8% of infants of Quebec as macrosomic. The Cree population are more at risk of fetal macrosomia, compared to the general population of Quebec, these associations were statistically significant: OR = 5.2; 95% CI (4.6 to 6.0) for birth weight> 4000g, OR = 8.1; 95% CI (6.2 to 10.7) for birth weight> 4500g and OR = 6.2; 95% CI (5.7 to 6.7) for birth weight percentile ≥90th Kramer. The risk of major perinatal morbidity associated with fetal macrosomia, is generally less important for the Cree than for the general population of Quebec: 0.76; 95% CI 0.62-0.94. Fetal macrosomia should be described by birth weight ≥95th percentile of Kramer, for the Cree, but preferably at the 90th percentile of the specific postnatal curves of Cree populations of Eastern James Bay. The specific Cree birth weight thresholds for diagnosing fetal macrosomia, at the 90th percentile of the 40th week of gestation, are 4 417g for the girls and 4 488g for the boys. Conclusion: Kramer’s curves diagnose systematically too much macrosomic Cree babies compare to the general population of Quebec. Futhermore, the risk of major maternal and perinatal morbidity is lower for these indigenous communities, at the different definitions of fetal macrosomia, suggesting the use of specific curves for the Cree, to reduce obstetrics interventions not required in large, but non macrosomic, Cree babies.

The problem of this study was to determine the value of Scholastic Aptitude Test scores and high school percentile rank for predicting a student's achievement in American history at North Texas State University. The study also sought to determine what, if any, difference existed between male and female students, students of different ethnic backgrounds, and students of different semester classification with respect to learning achievement in American history.

This paper holds a study of Swedish inequality from 1900-1985 with specific focus on the half-decades of 1900-1905 and 1980-1985. Subsequently constructed data and contemporary news outlets are presented to develop further understanding upon how inequality was depicted in comparison to data. Through a comparison of the time-periods, the developed understanding and changed stance of the public on the issue of inequality is examined. This method of examination gives new insight upon how the widening knowledge of inequality during the 1900s, through the development of micro-economic measurements, as well as more complete tax returns, has affected the depiction of the issue. The results of the study suggest that news articles of the latter period (1980-1985), tend to be more data-based than during the former time-period, where general assumptions were more frequent. It additionally suggests that the decreased inequality over the 20th century did not lessen the discussion of inequality, but rather the opposite. The news articles furthermore do not discuss inequality in relation to the presented data - the long-term changes are not clearly stated in the news outlets - but are in conclusion unconsciously considered, through the general knowledge of current inequality, through tax levels etc.