Consider a single-server queueing system with an unreliable server and service repetition. In this system, if the service is interrupted, the service is restarted anew immediately and ends whenever the service period is failure free. In this paper, we give some characterization of the exponential distribution by the constancy of total service time in this system. The result can be viewed as a kind of memoryless property of the exponential distribution.

The current trends of mobile battery-powered devices make area and power critical design constraints in many applications. It is important that embedded software implementations execute any given task as power efficiently as possible. These tasks often require the computation of transcendental functions (sine, cosine, exponential, logarithm, etc.). The CORDIC algorithm can be used to implement an area-efficient hardware accelerator to assist in the computation of many of these functions while reducing the total energy consumed. This report presents the design and implementation of a fixed-point CORDIC rotator. The CORDIC rotator is used to assist in the computation of IEEE-754 single-precision floating-point exponentials. Power simulation results show the CORDIC-assisted exponent computation consumes 81.42% less energy as compared with the unassisted software solution while adding less than 10% to the gate count of the original system. / text

The exponential model of Bloomfield (1973) is becoming increasingly important due to its recent applications to long memory time series. However, this model has received little consideration in the context of short memory time series. Furthermore, there has been very little attempt at using the EXP model as a model to analyze observed time series data. This dissertation research is largely focused on developing new methods to improve the utility and robustness of the EXP model. Specifically, a new nonparametric method of parameter estimation is developed using wavelets. The advantage of this method is that, for many spectra, the resulting parameter estimates are less susceptible to biases associated with methods of parameter estimation based directly on the raw periodogram. Additionally, several methods are developed for the validation of spectral models. These methods test the hypothesis that the estimated model provides a whitening transformation of the spectrum; this is equivalent to the time domain notion of producing a model whose residuals behave like the residuals of white noise. The results of simulation and real data analysis are presented to illustrate these methods.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1952. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 68-69).

Thesis (M.Phil.)--University of Hong Kong, 2003. / Includes bibliographical references (leaves 52) Also available in print.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Economics, 1994. / Title from PDF title page (viewed on Dec. 14, 2005) Available through DSpace, MIT Libraries' online institutional repository. Includes bibliographical references.

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O objetivo deste trabalho é fazer uma revisão dos modelos não lineares de família exponencial (Cordeiro & Paula (1989); Wei (1998)) para respostas independentes e apresentar possíveis extensões para o caso de dados correlacionados. Inicialmente são apresentados exemplos ilustrativos, alguns dos quais são reanalizados ao longo do texto. Em seguida são discutidos procedimentos de estimação e testes de hipóteses, tais como apresentação de um processo de estimação que pode ser adaptado ao processo iterativo usado na classe dos modelos lineares generalizados, e alguns resultados assintóticos. Técnicas usuais de diagnóstico, como pontos de alavanca, análise de resíduos e diagnóstico de influência são adaptados para a classe dos modelos não lineares de família exponencial. Extensões para a classe dos modelos não lineares com resposta binomial negativa são também apresentadas. Finalmente, são consideradas duas possíveis extensões dos modelos não lineares de família exponencial para dados correlacionados, através de equações de estimação generalizadas e através de modelagem mista em que efeitos aleatórios em forma linear são adicionados ao componente não linear da parte sistemática do modelo conforme sugerido recentemente por Tang et al. (2006a). / The aim of this work is to present a review of the exponential family nonlinear models (Cordeiro & Paula (1989); Wei (1998)) for independent responses and to present possible extensions for the case of correlated data. Firstly, ilustrative examples are presented with some of them being reanalyzed along the text. Then, estimation and hypothesis testing procedures, such as the presentation of an iterative process adapted from the one of generalized linear models, and some asymptotic results are discussed. Useful diagnostic techniques, as calculation of leverage measures, residual analysis and influence diagnostics are adapted for the class of exponential family nonlinear models. Extensions to nonlinear negative binomial models are also presented. Finally, two possible extensions for correlated data are considered, by using generalized estimating equations and mixed modeling in which linear random effects are added into the systematic component together with the nonlinear function, as suggested by Tang et al. (2006a).

In this diploma thesis we will introduce six de nitions of the natural exponential function and ve de nitions of the natural logarithmic function. We will prove the de nitions' correctness, derive basic properties of both funcions and show the equivalence of all de nitions for each function. We will see how these funcions are de ned in some textbooks for universities and in textbooks for grammar schools. We will discuss the bene ts and drawbacks of all de nitions and will use the criteria such as required theory and difficulty or length of proofs. At the end of the thesis we will make some recommendations regarding de ning these functions at high schools and universities and we will give several suggestions for an additional research.

No description available.