在生態學及生物學的研究中，「物種個數」(Number of Species)通常是「生物多樣性」(Species Diversity)的重要測量值，物種個數的多寡、分布與多樣性有相當的關聯。「物種」的概念不侷限於生物，舉凡網路搜尋引擎(Search Engine)使用的關鍵字詞、圖書館分類的數目種類、國際疾病代碼等，都可視為物種。 本文著眼於寫作風格的比較，研究中國知名小說「紅樓夢」，主要探討前八十回與後四十回是否為同一個作者，以估計物種個數的觀點作為寫作風格的比較標準，並以金庸的武俠小說為對照組，驗證分析的結果。本文除了使用除了Efron and Thisted的隨機模型，也考慮藉由區塊抽樣估計母體種類數之Jackknife、Bootstrap、Chao(1992)等估計方法。研究發現Efron and Thisted的模型的估計量容易呈現不穩定的震盪，可能會有無法收歛的問題；而Bootstrap、Jackknife與Chao(1992)則會有高估母體種類數的現象。利用涵蓋機率的概念發現Jackknife與Chao皆在抽出特定比例的樣本數時，估計值涵蓋母體種類數之機率值非常接近1。 / The number of species is frequently used to measure the species diversity of a population in studying ecology and biology. There are such relationships between numbers of species and its diversities. The idea of species diversity is not restricted to biology, it receives more applications in recent years. For example, the applications also include key words in search engines, classification's numbers in a library, and disease types in Measuring health. This article studies the well-known Chinese novel “The Dream of Red Chamber”, and the goal is to study whether the first 80 and last 40 chapters are from the same author. In particular, methods related the number of species are used to evaluate the goal of study. Also, some Chinese martial novels, by the famous writer Jin Yong, are used as the control group for the methods used. Methods considered in this study include Efron and Thisted’s Model, Jackknife, Bootstrap, estimation method from Chao (1992). We found that Efron and Thisted’s estimates tend to be less stable and slow in convergence. On the other hand, the estimates of Jackknife, Bootstrap, and Chao are likely to be over-biased. However, after some modifications, we found that the Jackknife and Chao’s estimates can be used to provide reliable predictions for the number of species of a finite population, given that part of the population is observed.

The increasing complexity of heterogeneous cellular networks (HetNets) due to the irregular deployment of small cells demands significant rethinking in the way cellular networks are perceived, modeled and analyzed. In addition to threatening the relevance of classical models, this new network paradigm also raises questions regarding the feasibility of state-of-the-art simulation-based approach for system design. This dissertation proposes a fundamentally new approach based on random spatial models that is not only tractable but also captures current deployment trends fairly accurately. First, this dissertation presents a general baseline model for HetNets consisting of K different types of base stations (BSs) that may differ in terms of transmit power, deployment density and target rate. Modeling the locations of each class of BSs as an independent Poisson Point Process (PPP) allows the derivation of surprisingly simple expressions for coverage probability and average rate. One interpretation of these results is that adding more BSs or tiers does not necessarily change the coverage probability, which indicates that fears of "interference overload" in HetNets are probably overblown. Second, a flexible notion of BS load is incorporated by introducing a new idea of conditionally thinning the interference field. For this generalized model, the coverage probability is shown to increase when lightly loaded small cells are added to the existing macrocellular networks. This is due to the fact that owing to the smaller loads, small cells typically transmit less often than macrocells, thus contributing less to the interference power. The same idea of conditional thinning is also shown to be useful in modeling the non-uniform user distributions, especially when the users lie closer to the BSs. Third, the baseline model is extended to study multi-antenna HetNets, where BSs across tiers may additionally differ in terms of the number of transmit antennas, number of users served and the multi-antenna transmission strategy. Using novel tools from stochastic orders, a tractable framework is developed to compare the performance of various multi-antenna transmission strategies for a fairly general spatial model, where the BSs may follow any general stationary distribution. The analysis shows that for a given total number of transmit antennas in the network, it is preferable to spread them across many single-antenna BSs vs. fewer multi-antenna BSs. Fourth, accounting for the load on the serving BS, downlink rate distribution is derived for a generalized cell selection model, where shadowing, following any general distribution, impacts cell selection while fading does not. This generalizes the baseline model and all its extensions, which either ignore the impact of channel randomness on cell selection or lumps all the sources of randomness into a single random variable. As an application of these results, it is shown that in certain regimes, shadowing naturally balances load across various tiers and hence reduces the need for artificial cell selection bias. Fifth and last, a slightly futuristic scenario of self-powered HetNets is considered, where each BS is powered solely by a self-contained energy harvesting module that may differ across tiers in terms of the energy harvesting rate and energy storage capacity. Since a BS may not always have sufficient energy, it may not always be available to serve users. This leads to a notion of availability region, which characterizes the fraction of time each type of BS can be made available under variety of strategies. One interpretation of this result is that the self-powered BSs do not suffer performance degradation due to the unreliability associated with energy harvesting if the availability vector corresponding to the optimal system performance lies in the availability region. / text

Skewness and kurtosis are measures used to describe shape characteristics of distributions. In this thesis, we examine the interval estimates about the skewness and kurtosis by using jackknife empirical likelihood (JEL), adjusted JEL, extended JEL, traditional bootstrap, percentile bootstrap, and BCa bootstrap methods. The limiting distribution of the JEL ratio is the standard chi-squared distribution. The simulation study of this thesis makes a comparison of different methods in terms of the coverage probabilities and interval lengths under the standard normal distribution and exponential distribution. The proposed adjusted JEL and extended JEL perform better than the other methods. Finally we illustrate the proposed JEL methods and different bootstrap methods with three real data sets.

With the advancement in the current wireless technology standards such as terrestrial digital video broadcasting systems (DVB-T, DVB-T2, and DVB-H) and the massive usage of the Internet over mobile devices, streaming of television channels in smart phones has become a necessary advancement for mobile users. As, UMTS dominating the entire mobile market globally and with the evolution of LTE, several mobile operators are working on an MBMS framework which will help to launch mobile TV services on respective operators. This paper deals with terrestrial and mobile TV with IP multicasting and broadcasting and is aimed to improve system spectral efficiency.  With the help of IP multicasting, the base station can be able to provide with significantly less spectrum by saving it from the channels which the user is not viewing currently. This case is analysed from several sets, called schemes of resource plan sets. The transmitter scheduling is dealt with by means of a Packet and Resource Plan Scheduling (PARPS) algorithm, and the simulated results are plotted in Matlab which assists in analysing the efficiency in the spectrum management and the coverage probability for the number of transmitters used for each scheme. The schemes are simulated in Matlab for different number of transmitters (2-7) in both the static and random model. The SFN schemes are offering greater coverage probability than MFN schemes, in all cases. Multicasting over Continuous Transmission Dynamic Single Frequency Network (CT-DSFN) offers a 1342% and 582% gain in Multi-user System Spectral Efficiency (MSSE) for 7 transmitters, from Broadcasting over MFN and Broadcasting over SFN respectively.  For 7 transmitters, Multicasting over CT-DSFN offers a 1213% and 428% gain in System Spectral Efficiency (SSE) from Broadcasting over MFN and Broadcasting over SFN respectively.

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Vehicular communication networks are essential to the development of intelligent navigation systems and improvement of road safety. Unlike most terrestrial networks of today, vehicular networks are characterized by stringent reliability and latency requirements. In order to design efficient networks to meet these requirements, it is important to understand the system-level performance of vehicular networks. Stochastic geometry has recently emerged as a powerful tool for the modeling and analysis of wireless communication networks. However, the canonical spatial models such as the 2D Poisson point process (PPP) does not capture the peculiar spatial layout of vehicular networks, where the locations of vehicular nodes are restricted to roadways. Motivated by this, we consider a doubly stochastic spatial model that captures the spatial coupling between the vehicular nodes and the roads and analyze the performance of vehicular communication networks. We model the spatial layout of roads by a Poisson line process (PLP) and the locations of nodes on each line (road) by a 1D PPP, thereby forming a Cox process driven by a PLP or Poisson line Cox process (PLCP). In this dissertation, we develop the theory of the PLCP and apply it to study key performance metrics such as coverage probability and rate coverage for vehicular networks under different scenarios. First, we compute the signal-to-interference plus noise ratio (SINR)-based success probability of the typical communication link in a vehicular ad hoc network (VANET). Using this result, we also compute the area spectral efficiency (ASE) of the network. Our results show that the optimum transmission probability that maximizes the ASE of the network obtained for the Cox process differs significantly from that of the conventional 1D and 2D PPP models. Second, we calculate the signal-to-interference ratio (SIR)-based downlink coverage probability of the typical receiver in a vehicular network for the cellular network model in which each receiver node connects to its closest transmitting node in the network. The conditioning on the serving node imposes constraints on the spatial configuration of interfering nodes and also the underlying distribution of lines. We carefully handle these constraints using various fundamental distance properties of the PLCP and derive the exact expression for the coverage probability. Third, building further on the above mentioned works, we consider a more complex cellular vehicle-to-everything (C-V2X) communication network in which the vehicular nodes are served by roadside units (RSUs) as well as cellular macro base stations (MBSs). For this setup, we present the downlink coverage analysis of the typical receiver in the presence of shadowing effects. We address the technical challenges induced by the inclusion of shadowing effects by leveraging the asymptotic behavior of the Cox process. These results help us gain useful insights into the behavior of the networks as a function of key network parameters, such as the densities of the nodes and selection bias. Fourth, we characterize the load on the MBSs due to vehicular users, which is defined as the number of vehicular nodes that are served by the MBS. Since the limited network resources are shared by multiple users in the network, the load distribution is a key indicator of the demand of network resources. We first compute the distribution of the load on MBSs due to vehicular users in a single-tier vehicular network. Building on this, we characterize the load on both MBSs and RSUs in a heterogeneous C-V2X network. Using these results, we also compute the rate coverage of the typical receiver in the network. Fifth and last, we explore the applications of the PLCP that extend beyond vehicular communications. We derive the exact distribution of the shortest path distance between the typical point and its nearest neighbor in the sense of path distance in a Manhattan Poisson line Cox process (MPLCP), which is a special variant of the PLCP. The analytical framework developed in this work allows us to answer several important questions pertaining to transportation networks, urban planning, and personnel deployment. / Doctor of Philosophy / Vehicular communication networks are essential to the development of intelligent transportation systems (ITS) and improving road safety. As the in-vehicle sensors can assess only their immediate environment, vehicular nodes exchange information about critical events, such as accidents and sudden braking, with other vehicles, pedestrians, roadside infrastructure, and cellular base stations in order to make critical decisions in a timely manner. Considering the time-sensitive nature of this information, it is of paramount importance to design efficient communication networks that can support the exchange of this information with reliable and high-speed wireless links. Typically, prior to actual deployment, any design of a wireless network is subject to extensive analysis under various operational scenarios using computer simulations. However, it is not viable to rely entirely on simulations for the system design of highly complex systems, such as the vehicular networks. Hence, it is necessary to develop analytical methods that can complement simulators and also serve as a benchmark. One of the approaches that has gained popularity in the recent years for the modeling and analysis of large-scale wireless networks is the use of tools from stochastic geometry. In this approach, we endow the locations of wireless nodes with some distribution and analyze various aspects of the network by leveraging the properties of the distribution. Traditionally, wireless networks have been studied using simple spatial models in which the wireless nodes can lie anywhere on the domain of interest (often a 1D or a 2D plane). However, vehicular networks have a unique spatial geometry because the locations of vehicular nodes are restricted to roadways. Therefore, in order to model the locations of vehicular nodes in the network, we have to first model the underlying road systems. Further, we should also consider the randomness in the locations of vehicles on each road. So, we consider a doubly stochastic model called Poisson line Cox process (PLCP), in which the spatial layout of roads are modeled by random lines and the locations of vehicles on the roads are modeled by random set of points on these lines. As is usually the case in wireless networks, multiple vehicular nodes and roadside units (RSUs) operate at the same frequency due to the limited availability of radio frequency spectrum, which causes interference. Therefore, any receiver in the network obtains a signal that is a mixture of the desired signal from the intended transmitter and the interfering signals from the other transmitters. The ratio of the power of desired signal to the aggregate power of the interfering signals, which is called as the signal-to-interference ratio (SIR), depends on the locations of the transmitters with respect to the receiver. A receiver in the network is said to be in coverage if the SIR measured at the location of the receiver exceeds the required threshold to successfully decode the message. The probability of occurrence of this event is referred to as the coverage probability and it is one of the fundamental metrics that is used to characterize the performance of a wireless network. In our work, we have analytically characterized the coverage probability of the typical vehicular node in the network. This was the first work to present the coverage analysis of a vehicular network using the aforementioned doubly stochastic model. In addition to coverage probability, we have also explored other performance metrics such as data rate, which is the number of bits that can be successfully communicated per unit time, and spectral efficiency. Our analysis has revealed interesting trends in the coverage probability as a function of key system parameters such as the density of roads in a region (total length of roads per unit area), and the density of vehicles on the roads. We have shown that the vehicular nodes in areas with high density of roads have lower coverage than those in areas with sparsely distributed roads. On the other hand, the coverage probability of a vehicular node improves as the density of vehicles on the roads increases. Such insights are quite useful in the design and deployment of network infrastructure. While our research was primarily focused on communication networks, the utility of the spatial models considered in these works extends to other areas of engineering. For a special variant of the PLCP, we have derived the distribution of the shortest path distance between an arbitrary point and its nearest neighbor in the sense of path distance. The analytical framework developed in this work allows us to answer several important questions pertaining to infrastructure planning and personnel deployment.

本論文共一冊，分八章八節。 內容：本論文所擬探討之對象為多變量統計分配函數模擬（Simulation）之最佳停止 法則問題（Optimal Stopping Rule Problem ），此類問題之目的在於如何利用盡量 小的樣本數之觀察值來求得未知母數（Unknoron Parameter）的信區間（域）（Co－ nfidence interval ）（Confidence Region），而此信賴區間（域）之寬度（Width ）及包含機率（Coverage Probability）均已事先指定。 以往研究對象多傴限於單變量統計分配函數，而多變量統計分配函數模擬之最佳停止 法則問題，仍尚在研究階段，因此本論文之重點乃在於探討如何求得滿足最佳停止法 則之最小樣本數。在此以多變量常態分配函數為重心，並進而嗜試推廣至其他多數量 統計分配函數。

傳統上，判定一種學名藥(generic drug)與原廠藥(innovator drug)是否具有生體相等性所常用的統計方法為：比較兩種藥物的生體可用相對值(relative bioavailability)的母體平均數是否相等，此即所謂的平均生體相等性(average bioequivalence)。然而就兩種藥物可互用的觀點而言，似乎更需要考慮的是每位受測個體在服用藥物後，不同藥物在個體內反應的差異性，因此 Anderson and Hauck (1990)提出個體生體相等性(individual bioequivalence)的觀點。 本文採 Schall (1995)所建議的判定準則來作為評估一種學名藥與原廠藥是否具有個體生體相等性的依據。內容重點為透過模擬(simulation)實驗的方式，對判定藥物為個體生體相等性的檢定力(power)作一評比，研究的項目有：(1)檢定力在不同交叉實驗設計(crossover design)下表現的異同；(2)檢定力在不同參數組合情況下表現的趨勢；(3)樣本數(sample size)對檢定力的影響。 / Conventionally, that a generic drug and an innovator drug are regarded as having the same treatment effects is based on the concept of average bioequivalence,i.e., that average responses between individuals on the two formulations are similar. Anderson and Hauck (1990) argued that it was not sufficient to expect that an individual patient would response similarly to the two formulations. The thought has received a lot of attention lately, and quite a few methods have been proposed to deal with the issue of the individual bioequivalence. According to the "unified" approach proposes by Schall (1995), a simulation study on power to declare bioequivalence and coverage probability of confidence intervals is carried out here to compare their performance under different experimental designs.

Made available in DSpace on 2016-06-02T20:06:01Z (GMT). No. of bitstreams: 1 2197.pdf: 1979337 bytes, checksum: 0091ce4138b8a98277d9af0d5d2aa788 (MD5) Previous issue date: 2008-11-13 / Universidade Federal de Sao Carlos / In this dissertation we present a regression modelling proposal for modelling the market prices of urban batches at São Carlos city (SP), over the year of 2005. Usual regression modelling and survival techniques, with left censoring, are considered. A simulation study exames the coverage probabilities the asymptotic confidence for the parameters of the considered modelling. / Nesta disertação apresentaremos uma proposta de um modelo de equação de regressão representativa para a formação do valor de mercado dos lotes urbanos do município de São Carlos, SP, ano de 2005, visando à criação de Plantas de Valores Genéricos (PVG) utilizando as técnicas de: Modelos Lineares Usuais (erros normais e variância constante), estes amplamente utilizados, e a Análise de Sobrevivência com censura à esquerda. Após o ajuste, as duas metodologias são comparadas e testadas num estudo de simulação onde examinamos a probabilidade de cobertura de alguns parâmetros envolvidos na regressão.