There has been widespread concern expressed by members of the statistics education community in the past few years about the lack of any real understanding demonstrated by many students completing courses in introductory statistics. This deficiency in understanding has been particularly noted in the area of inferential statistics, where students, particularly those studying statistics as a service course, have been inclined to view statistical inference as a set of unrelated recipes. As such, these students have developed skills that have little practical application and are easily forgotten. This thesis is concerned with the development of understanding in statistical inference for beginning students of statistics at the post-secondary level. This involves consideration of the nature of understanding in introductory statistical inference, and how understanding can be measured in the context of statistical inference. In particular, the study has examined the role of the sampling distribution in the students? schemas for statistical inference, and its relationship to both conceptual and procedural understanding. The results of the study have shown that, as anticipated, students will construct highly individual schemas for statistical inference but that the degree of integration of the concept of sampling distribution within this schema is indicative of the level of development of conceptual understanding in that student. The results of the study have practical implications for the teaching of courses in introductory statistics, in terms of content, delivery and assessment.

This work investigates the tensile behaviour of non-uniform fibres and fibrous composites. Wool fibres are used as an example of non-uniform fibres because they're physical, morphological and geometrical properties vary greatly not only between fibres but also within a fibre. The focus of this work is on the effect of both between-fibre and within-fibre diameter variations on fibre tensile behaviour. In addition, fit to the Weibull distribution by the non-brittle and non-uniform visco-elastic wool fibres is examined, and the Weibull model is developed further for non-uniform fibres with diameter variation along the fibre length. A novel model fibre composite is introduced to facilitate the investigation into the tensile behaviour of fibre-reinforced composites. This work first confirms that for processed wool, its coefficient of variation in break force can be predicted from that of minimum fibre diameters, and the prediction is better for longer fibres. This implies that even for processed wool, fibre breakage is closely associated with the occurrence of thin sections along a fibre, and damage to fibres during processing is not the main cause of fibre breakage. The effect of along-fibre diameter variation on fibre tensile behaviour of scoured wool and mohair is examined next. Only wet wool samples were examined in the past. The extensions of individual segments of single non-uniform fibres are measured at different strain levels. An important finding is the maximum extension (%) (Normally at the thinnest section) equals the average fibre extension (%) plus the diameter variation (CV %) among the fibre segments. This relationship has not been reported before. During a tensile test, it is only the average fibre extension that is measured. The third part of this work is on the applicability of Weibull distribution to the strength of non-uniform visco-elastic wool fibres. Little work has been done for wool fibres in this area, even though the Weibull model has been widely applied to many brittle fibres. An improved Weibull model incorporating within-fibre diameter variations has been developed for non-uniform fibres. This model predicts the gauge length effect more accurately than the conventional Weibull model. In studies of fibre-reinforced composites, ideal composite specimens are usually prepared and used in the experiments. Sample preparation has been a tedious process. A novel fibre reinforced composite is developed and used in this work to investigate the tensile behaviour of fibre-reinforced composites. The results obtained from the novel composite specimen are consistent with that obtained from the normal specimens.

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Individuals within a species often compete for resources in both space and time. In dominance hierarchies individuals with the greatest competitive ability will occupy prime locations during optimal periods to increase efficiency in gathering a resource. Subdominant individuals with low competitive abilities may be forced to reside in habitats of poor quality relative to dominant individuals. In this study I examined the long term patterns of giant kokopu distribution, movement, growth, habitat use, and social interaction between fish in relation to invertebrate drift (food supply). The habitat quality and abundance of food along a one km section of Alex�s Creek was monitored for a two year period. Though the physical structure of Alex�s Creek was relatively homogenous there were significant spatial differences in the density of drifting invertebrates sampled between riffles and pools over this long temporal period. In general, more drifting invertebrates were sampled in riffles of relatively long length and area. Within Alex�s Creek the distribution of giant kokopu, Galaxias argenteus, was determined by patchy distributions of food supply, specific physical factors of pools, and interactions between fish in dominance hierarchies. Over the 20 month study period, the most important biotic factor determining fish biomass was the total number of drifting invertebrates within pools while the most important abiotic factor determining fish abundances within pools was the pool size (surface area). The growth rate of individual fish correspondingly varied between fish residing within pools of different quality. Growth rates were higher for individual fish residing in pools with a relatively high density of drifting invertebrates. The differences in individual growth rates of giant kokopu may determine when fish leave a particular habitat patch (pool) and move to a new one. Fish that moved had lower growth rates (before moving) than fish that remained resident within home pools. Overall the movement of giant kokopu within Alex�s Creek was very restricted due to a relatively consistent distribution of food, however there were differences in the mobility of giant kokopu among different social ranks. The most dominant fish in pools were largely sedentary while fish ranked directly below fish 1 (i.e. fish 2 and 3 in social hierarchies) were relatively mobile. The ability of dominant fish to exclude subdominant fish from the most preferred feeding positions during optimal feeding times had consequences for overall giant kokopu activity. Under normal food supply conditions dominant fish were predominantly nocturnal and maintained large home ranges at night. Conversely subdominant fish occupied large home ranges by day, but were generally not observed at night. When the food supply was limited the utilization of pools was determined by social rank. Dominant fish from each pool increased daytime activity, home range size, aggressiveness, and the capture of food items offered by day while simultaneously reducing the spatial and temporal activity and habitat use of subdominant fish. These results indicate that behavioral changes in large dominant fish influence and reduce the amount of resources available to subdominant fish.

一方面，儘管相較於許多歐美國家而言，我國所得分配不均的程度較小，但不可否認地，我國目前正處於所得分配惡化的年代，另一方面，在政府做了這許多看似有利於民的德政後，究竟發揮了多少預期的功效？究竟對所得分配的改善有無肋益？ 有鑑於此，本文針對我國八十五年政府的財政收支的所得重分配效果進行分析與研究，以期瞭解政府財政收支之所得重分配效果。不過，在內容上，由於以往國內外文獻多只探討租稅或支出面，故本文兼顧租稅及支出兩方面，而在方法上，歸納以往國內外文獻所採用之方法不外乎歸宿假設與衡量指標兩種，其中又多以歸宿假設為主，少以衡量指標為主，因此，本文跳脫出以往方法上的侷限，兼採歸宿假設與衡量指標兩種方法，並以目前國內文獻尚未採用之RSA衡量指標進行實證研究。實證結果顯示，不論是採有效稅率及有效受益率抑或是採RSA衡量指標進行分析，皆可發現：1•租稅方面在中央政府租稅中，以綜合所得稅的所得重分配效果最大，而以公賣利益的所得重分配效果最小，且有負效果；在地方政府租稅中，則以土地增值稅的所得重分配效果最大，而以營業稅的所得重分配效果最小，且有負效果。整體而言，中央政府租稅的所得重分配效果較地方政府租稅為大。2•支出方面在中央政府支出中，以國防支出的所得重分配效果最大，而以退休撫卹支出的所得重分配效果最小，且有負效果；在地方政府支出中，則以教科文支出的所得重分配效果最大，而以經濟發展支出的所得重分配效果最小，但仍為正效果。整體而言，中央及地方政府支出皆具有所得重分配效果，且其中又以地方政府支出的所得重分配效果較中央政府支出為大。3•財政收支雖然直接稅具有某種程度的所得重分配效果，但其中只有佔我國總租稅收入比重30％的綜合所得稅及營利事業所得稅的得重分配效果較顯著，而佔我國總租稅收入比重46％的間接稅卻有負效果。因此，我國租稅整體而言並不具有改善所得分配的效果。不過，由於我國政府支出對所得分配的改善有顯著而正面的效果，因此，我國八十五年政府財政收支對於所得分配的改善仍具有相當的貢獻。

無 / We derive the MacLaurin series for the moments of the idle time with respect to the parameters in the service time and interarrival time distributions for a GI/G/I queue. The light traffic derivatives are obtained to investigate the quality of a well-known MacLaurin series. The coefficients in these series are expressed in terms of the derivatives of the interarrival time density function evaluated at zero and the moments of the service time distribution, which can be easily calculated through a simple recursive procedure. The result for the idle period is easily taken as input to the calculation of other performance measures of the system, e.g., interdeparture time distributions. Numerical examples are given to illustrate these results.

在眾多產生貝他分配的方法中，我們研究Kennedy的演算法。在本文中，我們探討在小樣本下，不同參數組合(k,p,q,r) 產生同一貝他分配的情形。 / There are mAny methods for generating a beta distribution. In this study, we focus on the method proposed by Kennedy (1988). Let [A₁,B₁]=[0,1] And [A_n,B_n] be rAndom subinterval of [0,1] defined recursively as follows. Take C , D to be the minimum And maximum of k i.i.d rAndom points uniformly distributed on [A_n,B_n]; And choose [A_n+1,B_n+1] to be [C_n,B_n], [A_n,D_n] or [C_n,D_n] with probabilities p, q, r respectively such that p+q+r=1. Kennedy showed that the limiting distribution of [A_n,B_n] has a beta distribution on [0,1] with parameters k(p+r) And k(q+r). 　　Based upon the known asymptotic result, we study the small-sample behaviors among those combinations of k, p, q, r that have the same Beta(m, n) distribution, where m = k(p+r), n = k(q+r), through simulations. We conclude that smaller k's basically have better performAnces.

The distribution of economic wellbeing is generally regarded as one of the key performance indicators of a society and economic wellbeing is strongly influenced by income, wealth and consumption. Despite this, almost all studies of inequality in Australia have relied upon income as the sole measure of economic wellbeing, due in large part to the ready availability of income data. This thesis attempts to redress that deficiency. This thesis provides an insight into an under-researched but vitally important topic � the distribution of wealth. Specifically the research has three goals. The first is to provide estimates of the level and distribution of wealth in Australia at the current time and the trends over the past decade or two. The second aim is to provide projections of the future wealth distribution. The final goal is to see if there are significant differences between the distribution of lifetime wealth and the annual cross-sectional distribution of wealth. The research uses a technique not previously used in Australia to estimate wealth in the future � dynamic microsimulation. The microsimulation model used is based on a starting sample of 150,000 individuals and this large number allows a large range of experiences to be modelled, while not having the high costs, years of commitment and other problems associated with undertaking panel studies. This thesis estimates that the average levels of wealth will increase significantly over the 40-year period from 2000 to 2040 but that wealth inequality will increase over the same period. The reasons for the increases in wealth inequality appear to be due to changes in asset ownership, particularly lower levels of home ownership; the ageing population; and increases in inequality within age cohorts. The research found that lifetime wealth inequality for a sub-group of Generation X differed from the distribution based on annual data. The lifetime wealth inequality was significantly less than the annual wealth inequality.

Thesis (M.S.)--University of Missouri--Rolla, 2007. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed December 3, 2007) Includes bibliographical references (p. 29-31).

Thesis (M.S. in electrical engineering)--Washington State University, December 2007. / Includes bibliographical references (p. 57-58).