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Dissertations / Theses on the topic 'Distribution (probability theory)'

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Published: 4 June 2021

Last updated: 31 July 2024

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1

Elamir, Elsayed Ali Habib. "Probability distribution theory, generalisations and applications of L-moments." Thesis, Durham University, 2001. http://etheses.dur.ac.uk/3987/.

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In this thesis, we have studied L-moments and trimmed L-moments (TL-moments) which are both linear functions of order statistics. We have derived expressions for exact variances and covariances of sample L-moments and of sample TL-moments for any sample size n in terms of first and second-order moments of order statistics from small conceptual sample sizes, which do not depend on the actual sample size n. Moreover, we have established a theorem which characterises the normal distribution in terms of these second-order moments and the characterisation suggests a new test of normality. We have also derived a method of estimation based on TL-moments which gives zero weight to extreme observations. TL-moments have certain advantages over L-moments and method of moments. They exist whether or not the mean exists (for example the Cauchy distribution) and they are more robust to the presence of outliers. Also, we have investigated four methods for estimating the parameters of a symmetric lambda distribution: maximum likelihood method in the case of one parameter and L-moments, LQ-moments and TL-moments in the case of three parameters. The L-moments and TL-moments estimators are in closed form and simple to use, while numerical methods are required for the other two methods, maximum likelihood and LQ-moments. Because of the flexibility and the simplicity of the lambda distribution, it is useful in fitting data when, as is often the case, the underlying distribution is unknown. Also, we have studied the symmetric plotting position for quantile plot assuming a symmetric lambda distribution and conclude that the choice of the plotting position parameter depends upon the shape of the distribution. Finally, we propose exponentially weighted moving average (EWMA) control charts to monitor the process mean and dispersion using the sample L-mean and sample L-scale and charts based on trimmed versions of the same statistics. The proposed control charts limits are less influenced by extreme observations than classical EWMA control charts, and lead to tighter limits in the presence of out-of-control observations.

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2

Bright, Leslie William. "Matrix-analytic methods in applied probability /." Title page, table of contents and abstract only, 1996. http://web4.library.adelaide.edu.au/theses/09PH/09phb855.pdf.

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3

Jónsson, Ragner H. "Adaptive subband coding of video using probability distribution models." Diss., Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/14453.

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4

Słowiński, Witold. "Autonomous learning of domain models from probability distribution clusters." Thesis, University of Aberdeen, 2014. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=211059.

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Nontrivial domains can be difficult to understand and the task of encoding a model of such a domain can be difficult for a human expert, which is one of the fundamental problems of knowledge acquisition. Model learning provides a way to address this problem by allowing a predictive model of the domain's dynamics to be learnt algorithmically, without human supervision. Such models can provide insight about the domain to a human or aid in automated planning or reinforcement learning. This dissertation addresses the problem of how to learn a model of a continuous, dynamic domain, from sensory observations, through the discretisation of its continuous state space. The learning process is unsupervised in that there are no predefined goals, and it assumes no prior knowledge of the environment. Its outcome is a model consisting of a set of predictive cause-and-effect rules which describe changes in related variables over brief periods of time. We present a novel method for learning such a model, which is centred around the idea of discretising the state space by identifying clusters of uniform density in the probability density function of variables, which correspond to meaningful features of the state space. We show that using this method it is possible to learn models exhibiting predictive power. Secondly, we show that applying this discretisation process to two-dimensional vector variables in addition to scalar variables yields a better model than only applying it to scalar variables and we describe novel algorithms and data structures for discretising one- and two-dimensional spaces from observations. Finally, we demonstrate that this method can be useful for planning or decision making in some domains where the state space exhibits stable regions of high probability and transitional regions of lesser probability. We provide evidence for these claims by evaluating the model learning algorithm in two dynamic, continuous domains involving simulated physics: the OpenArena computer game and a two-dimensional simulation of a bouncing ball falling onto uneven terrain.

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5

Pashley, Peter J. "The analysis of latency data using the inverse Gaussian distribution /." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75343.

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The inverse Gaussian distribution is investigated as a basis for statistical analyses of skewed and possibly censored response times. This distribution arises from a random walk process, is a member of the exponential family, and admits the sample arithmetic and harmonic means as complete sufficient statistics. In addition, the inverse Gaussian provides a reasonable alternative to the more commonly used lognormal statistical model due to the attractive properties of its parameter estimates.
Three modifications were made to the basic distribution definition: adding a shift parameter to account for minimum latencies, allowing for Type I censoring, and convoluting two inverse Gaussian random variables in order to model components of response times. Corresponding parameter estimation and large sample test procedures were also developed.
Results from analysing two extensive sets of simple and two-choice reaction times suggest that shifting the origin and accounting for Type I censoring can substantially improve the reliability of inverse Gaussian parameter estimates. The results also indicate that the convolution model provides a convenient medium for probing underlying psychological processes.

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6

Cassady, Charles Richard. "The frequency distribution of availability." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-09052009-040624/.

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7

Ding, Xiqian, and 丁茜茜. "Some new statistical methods for a class of zero-truncated discrete distributions with applications." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2015. http://hdl.handle.net/10722/211126.

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Counting data without zero category often occur in various _elds. Examples include days of hospital stay for patients, numbers of publication for tenure-tracked faculty in a university, numbers of tra_c violation for drivers during a certain period and so on. A class of zero-truncated discrete models such as zero-truncated Poisson, zero-truncated binomial and zero-truncated negative-binomial distributions are proposed in literature to model such count data. In this thesis, firstly, literature review is presented in Chapter 1 on a class of commonly used univariate zero-truncated discrete distributions. In Chapter 2, a unified method is proposed to derive the distribution of the sum of i.i.d. zero-truncated distribution random variables, which has important applications in the construction of the shortest Clopper-Person confidence intervals of parameters of interest and in the calculation of the exact p-value of a two-sided test for small sample sizes in one sample problem. These problems are discussed in Section 2.4. Then a novel expectation-maximization (EM) algorithm is developed for calculating the maximum likelihood estimates (MLEs) of parameters in general zero-truncated discrete distributions. An important feature of the proposed EM algorithm is that the latent variables and the observed variables are independent, which is unusual in general EM-type algorithms. In addition, a unified minorization-maximization (MM) algorithm for obtaining the MLEs of parameters in a class of zero-truncated discrete distributions is provided. The first objective of Chapter 3 is to propose the multivariate zero-truncated Charlier series (ZTCS) distribution by developing its important distributional properties, and providing efficient MLE methods via a novel data augmentation in the framework of the EM algorithm. Since the joint marginal distribution of any r-dimensional sub-vector of the multivariate ZTCS random vector of dimension m is an r-dimensional zero-deated Charlier series (ZDCS) distribution (1 6 r < m), it is the second objective of Chapter 3 to propose a new family of multivariate zero-adjusted Charlier series (ZACS) distributions (including the multivariate ZDCS distribution as a special member) with a more flexible correlation structure by accounting for both inflation and deflation at zero. The corresponding distributional properties are explored and the associated MLE method via EM algorithm is provided for analyzing correlated count data.
published_or_final_version
Statistics and Actuarial Science
Master
Master of Philosophy

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8

Calhoun, Grayson Ford. "Limit theory for overfit models." Diss., [La Jolla] : University of California, San Diego, 2009. http://wwwlib.umi.com/cr/ucsd/fullcit?p3359804.

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Thesis (Ph. D.)--University of California, San Diego, 2009.
Title from first page of PDF file (viewed July 23, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 104-109).

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9

Shahriari, Shahriar. "The Frechet distribution as an alternative model of extreme value data." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26735.

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The Frechet distribution was applied to a set of earthquake data in order to test its validity as a practical alternative distribution for extreme value data. It was concluded that the Frechet distribution was the best model representing that data set. Also, a Poisson model of occurrence could not be rejected for that data set. The combination of these two models resulted in a closed form unconditional extreme value distribution which was developed analytically. The appropriate statistical tests and sensitivity analyses were performed on the obtained model.
Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate

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10

Mbah, Alfred Kubong. "On the theory of records and applications." [Tampa, Fla.] : University of South Florida, 2007. http://purl.fcla.edu/usf/dc/et/SFE0002216.

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11

李建德 and Kin-tak Christopher Li. "Statistical problems involving compositions in a covariate role." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1986. http://hub.hku.hk/bib/B31207777.

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Li, Kin-tak Christopher. "Statistical problems involving compositions in a covariate role /." [Hong Kong] : University of Hong Kong, 1986. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12326227.

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13

Anabila, Moses A. "Skew Pareto distributions." abstract and full text PDF (free order & download UNR users only), 2008. http://0-gateway.proquest.com.innopac.library.unr.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1453191.

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Stewart, Michael. "Asymptotic methods for tests of homogeneity for finite mixture models." Connect to full text, 2002. http://hdl.handle.net/2123/855.

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Thesis (Ph. D.)--University of Sydney, 2002.
Title from title screen (viewed Apr. 28, 2008). Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Mathematics and Statistics, Faculty of Science. Includes bibliography. Also available in print form.

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15

Brown, Nicole Dawn. "Reliability studies of the skew normal distribution." Fogler Library, University of Maine, 2001. http://www.library.umaine.edu/theses/pdf/BrownND2001.pdf.

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16

Ma, Kin-Keung. "Infinite prefix codes for geometric distributions /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?COMP%202004%20MA.

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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004.
Includes bibliographical references (leaves 74-76). Also available in electronic version. Access restricted to campus users.

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17

Forkéus, Ted. "Distribution of Critical Points of Polynomials." Thesis, Karlstads universitet, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-82941.

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This thesis studies the relationship between the zeroes of complexpolynomials in one variable and the critical points of those polynomials. Our methods are both analytical and statistical in nature, usingtechniques from both complex analysis and probability theory. Wepresent an alternative proof for the famous Gauss-Lucas theorem aswell as proving that the distribution for the critical points of a randompolynomial with real zeroes will converge in probability to the distribution of the zeroes. A simulation of the case with complex zeroesis also presented, which gives statistical support that this holds forrandom polynomials with complex zeroes as well. Lastly, the previous results are then applied to Sendov’s conjecture where we take aprobabilistic approach to this problem.

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18

Lai, Pik-ying, and 黎碧瑩. "Lp regression under general error distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B30287844.

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19

Wahed, Abdus S. "General families of skew-symmetric distributions." Virtual Press, 2000. http://liblink.bsu.edu/uhtbin/catkey/1178355.

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The family of univariate skew-normal probability distributions, an extension of symmetric normal distribution to a general case of asymmetry, was originally proposed by Azzalani [1]. Since its introduction, very limited research has been conducted in this area. An extension of the univariate skew-normal distribution to the multivariate case was considered by Azzalani and Dalla Valle [4]. Its application in statistics was recently considered by Azzalani and Capitanio [3]. As a general result, Azzalani (1985) [See [1]] showed that, any symmetric distribution can be viewed as a member of a more general class of skewed distributions.In this study we establish some properties of general family of skewed distributions. Examples of general family of asymmetric distributions is presented in a way to show their differences from the corresponding symmetric distributions. The skew-logistic distribution and its properties are considered in great details.
Department of Mathematical Sciences

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20

Majumder, M. Mahbubul A. "On Tukey's gh family of distributions." Virtual Press, 2007. http://liblink.bsu.edu/uhtbin/catkey/1371472.

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Skewness and elongation are two factors that directly determine the shape of a probability distribution. Thus, to obtain a flexible distribution it is always desirable that the parameters of the distribution directly determine the skewness and elongation. To meet this purpose, Tukey (1977) introduced a family of distributions called g-and-h family (gh family) based on a transformation of the standard normal variable where g and h determine the skewness and the elongation, respectively. The gh family of distributions was extensively studied by Hoaglin (1985) and Martinez and Iglewicz (1984). For its flexibility in shape He and Raghunathan (2006) have used this distribution for multiple imputations. Because of the complex nature of this family of distributions, it is not possible to have an explicit mathematical form of the density function and the estimates of the parameters g and h fully depend on extensive numerical computations.In this study, we have developed algorithms to numerically compute the density functions. We present algorithms to obtain the estimates of g and h using method of moments, quantile method and maximum likelihood method. We analyze the performance of each method and compare them using simulation technique. Finally, we study some special cases of gh family and their properties.
Department of Mathematical Sciences

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21

Spencer, Steven Robert. "Renewal theory for uniform random variables." CSUSB ScholarWorks, 2002. https://scholarworks.lib.csusb.edu/etd-project/2248.

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This project will focus on finding formulas for E[N(t)] using one of the classical problems in the discipline first, and then extending the scope of the problem to include overall times greater than the time t in the original problem. The expected values in these cases will be found using the uniform and exponential distributions of random variables.

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22

Feng, Jingyu. "Modeling Distributions of Test Scores with Mixtures of Beta Distributions." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1068.pdf.

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23

Sun, Yannan. "Extremal dependence of multivariate distributions and its applications." Pullman, Wash. : Washington State University, 2010. http://www.dissertations.wsu.edu/Dissertations/Spring2010/Y_SUN_041610.pdf.

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24

O'Connell, W. Richard Jr. "Estimates for the St. Petersburg game." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/28858.

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25

潘成達 and Shing-Tat Poon. "Measuring the degree of dependence of lifetimes in some bivariate survival distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31977443.

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26

Kan, Kin-fai, and 簡健輝. "Maintenance of partial-sum-based histograms." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B26635197.

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27

陳冠全 and Koon-chuen Chen. "Invariant limiting shape distributions for some sequential rectangularmodels." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B31238233.

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Poon, Shing-Tat. "Measuring the degree of dependence of lifetimes in some bivariate survival distributions." [Hong Kong] : University of Hong Kong, 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13787421.

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Chen, Koon-chuen. "Invariant limiting shape distributions for some sequential rectangular models /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20998934.

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30

Lopa, Samia H. "Dirac generalized function : an alternative to the change of variable technique." Virtual Press, 2000. http://liblink.bsu.edu/uhtbin/catkey/1179126.

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Finding the distribution of a statistic is always an important problem that we face in statistical inference. Methods that are usually used for solving this problem are change of variable technique, distribution function technique and moment generating function technique. Among these methods change of variable technique is the most commonly used one. This method is simple when the statistic is a one-to-one transformation of the sample observations and if it is many-to-one, then one needs to compute the jacobian for each partition of the range for which the transformation is one-to-one. In addition, if we want to find the distribution of a statistic involving n random variables using the change of variable technique, we have to define (n-1) auxiliary variables. Unless these (n-1) auxiliary variables are carefully chosen, calculation of jacobian as well as finding the range of integration to obtain the marginal distribution of the statistic of interest become complicated. [See [3]]Au, Chi and Tam, Judy [1] proposed an alternative method of finding the distribution of a statistic by using Dirac generalized function. In this study we considera number of problems involving different probability distributions that are not quiet easy to solve by change of variable technique. We will illustrate the method by solving problems which include finding the distributions of sums, products, differences and ratios of random variables. The main purpose of the thesis is to show that using Dirac generalized function one can solve these problems with more ease. This alternative approach would be more suitable for students with limited mathematical background.
Department of Mathematical Sciences

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31

Choi, Chun-sun. "Modelling the fat tail distribution of security market returns." Click to view the E-thesis via HKUTO, 1989. http://sunzi.lib.hku.hk/hkuto/record/B3197577X.

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32

King, Robert Arthur Ravenscroft. "New distributional fitting methods applied to the generalised [lambda] distribution." Thesis, Queensland University of Technology, 1999.

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33

Omran, Mohammed Fawzy. "Modelling the probability distribution of the time series stock price changes in the U.K. market." Thesis, University of Strathclyde, 1997. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=21370.

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The thesis considers different aspects of the probability distribution of the time series of stock price changes in the UK market. It places particular emphasis on the character of the volatility of the series. Chapter 2 documents some preliminary findings about changes in the FT-ALL share price index. These findings are: (1) its distribution has fat tails; (2) the BDS test rejects the hypothesis of identically, and independently distributed price changes; (3) the BDS test applied to the GARCH(l, 1) residuals, adjusted according to de Lima (1995b), indicates that Autoregressive Conditional Heteroscedasticity explains most of the nonlinearity in the FT-ALL price changes. The hypothesis of constant variance is rejected for the FT-ALL series using the Loretan and Phillips test, reported in chapter 3. An intervention model along the lines of Box and Tiao (1975) is used to model possible shifts in the variance of the FT-ALL price changes during the 1973 oil crisis and the 1987 market crash. The model allows for slow decay in the shocks effects and a different level of volatility after both crises. The results suggest that the reaction of the UK market to both crises differs only with regard to the slow decay of the shocks. The null hypothesis of constant variance is "accepted" for the residuals from the intervention model. This "acceptance" is due to the filtering of the effects of the 1973 and 1987 crisis from the FT-ALL series. The hypothesis that GARCH volatility persistence becomes insignificant when the volume of trade is included is examined in chapter 4. In a test covering the price behaviour of 57 UK companies over the period from 4/1/1988 to 28/2/1994, it is found that although the parameter estimates of the GARCH model becomes insignificant when volume is used in the conditional variance of price changes, the autocorrelations of the squared residuals still exhibit a highly significant GARCH pattern. It is argued that the GARCH-volume model of Lamoureux and Lastrapes (1990b) suffers from a multicollinearity problem, apart from the possible simultaneity bias which could lead to an inconsistent estimate of the parameter for volume. It is found that unexpected volume reduces volatility persistence. This reduction can be attributed to the strong association in the timing of innovational outliers in the price changes and unexpected volume found in the study. The results are consistent with the market depth hypothesis of Bessembinder and Seguin (1993). The GARCH model with the conditional normal, Student's t and generalized error distributions is estimated for the UK FT-ALL price changes in chapter 5. The model also considers seasonal and leverage effects. The time period for the study is chosen so as to avoid including the 1987 crash. The results suggest:( 1) volatility persistence is low after the 1987 crash; (2) the ARMA and ARCH effects, along with the seasonal effects of Monday and holidays, explain a significant part of the departure from normality; (3) there is a need for leptokurtic distribution such as the Student's t; and (4) there is no evidence for a leverage effect in the FT-ALL series. That is, positive and negative surprises tend to affect volatility in the same way.

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Hao, Jie. "Some New Probability Distributions Based on Random Extrema and Permutation Patterns." Digital Commons @ East Tennessee State University, 2014. https://dc.etsu.edu/etd/2344.

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In this paper, we study a new family of random variables, that arise as the distribution of extrema of a random number N of independent and identically distributed random variables X1,X2, ..., XN, where each Xi has a common continuous distribution with support on [0,1]. The general scheme is first outlined, and SUG and CSUG models are introduced in detail where Xi is distributed as U[0,1]. Some features of the proposed distributions can be studied via its mean, variance, moments and moment-generating function. Moreover, we make some other choices for the continuous random variables such as Arcsine, Topp-Leone, and N is chosen to be Geometric or Zipf. Wherever appropriate, we estimate of the parameter in the one-parameter family in question and test the hypotheses about the parameter. In the last section, two permutation distributions are introduced and studied.

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Lipson, Kay, and klipson@swin edu au. "The role of the sampling distribution in developing understanding of statistical inference." Swinburne University of Technology, 2000. http://adt.lib.swin.edu.au./public/adt-VSWT20050711.161903.

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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.

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Balabdaoui, Fadoua. "Nonparametric estimation of a k-monotone density : a new asymptotic distribution theory /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/8964.

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Chen, Yi-Ju. "Distribution results for certain tests based on ranks /." free to MU campus, to others for purchase, 1997. http://wwwlib.umi.com/cr/mo/fullcit?p9841272.

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Sitton, David E. R. "Generating random absolutely continuous distributions." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/28989.

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Zhang, Zuoshun. "Proper posterior distributions for some hierarchical models and roundoff effects in the Gibbs sampler /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.

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Unger, William Ramsay. "Asymptotics of increasing trees." Thesis, The University of Sydney, 1993. https://hdl.handle.net/2123/26633.

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This thesis addresses the problem of ﬁnding the asymptotic average path length in species of increasing trees. A version of Joyal’s theory of species, L—species, is used to derive power series identities for simple increasing trees and give them bijective proofs. The main identity involved here is an autonomous, nonlinear, ordinary differential equation. Asymptotic results on the number and average path length of these species are derived by analysis of the singularities of these power series when they are treated as analytic functions. The result is a general method for ﬁnding the asymptotic number of and asymptotic average path length in increasing trees deﬁned by a single differential equation. In the particular case Where there is a uniform upper bound on the number of descendents a vertex has (and in some other cases) the method can be simply automated using a symbolic algebra package such as MAPLE. It is found that the expected path length of a tree in a species of increasing trees with the above restriction is asymptotically proportional to n log n, where n is the number of vertices in the tree. By contrast, it is shown, using similar combinatorial methods, that labelled, non—increasing trees and unlabelled trees, to which similar analytic methods apply, have path length asymptotically proportional to n*sqrt(n).

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Ho, Pak-kei. "Parametric and non-parametric inference for Geometric Process." Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B31483859.

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Ho, Pak-kei, and 何柏基. "Parametric and non-parametric inference for Geometric Process." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B31483859.

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Wong, Hoi-lam. "On two tests for multivariate normality." HKBU Institutional Repository, 1993. https://repository.hkbu.edu.hk/etd_ra/12.

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Whaley, Dewey Lonzo. "The Interquartile Range: Theory and Estimation." Digital Commons @ East Tennessee State University, 2005. https://dc.etsu.edu/etd/1030.

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The interquartile range (IQR) is used to describe the spread of a distribution. In an introductory statistics course, the IQR might be introduced as simply the “range within which the middle half of the data points lie.” In other words, it is the distance between the two quartiles, IQR = Q3 - Q1. We will compute the population IQR, the expected value, and the variance of the sample IQR for various continuous distributions. In addition, a bootstrap confidence interval for the population IQR will be evaluated.

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Glus̆c̆ević, Vido. "Approximation for Csiszár f-divergence /." Title page, table of contents and summary only, 2004. http://web4.library.adelaide.edu.au/theses/09PH/09phg5678.pdf.

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46

Kam, Po-ling, and 甘寶玲. "Mixture autoregression with heavy-tailed conditional distribution." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B29614922.

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47

Lee, Gunhee. "Noninformative priors for some models useful in reliability and survival analysis /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9720544.

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48

Bataineh, Mohammad Saleh, University of Western Sydney, of Science Technology and Environment College, and of Science Food and Horticulture School. "Stochastic systems : models and polices [sic]." THESIS_CSTE_SFH_Bataineh_M.xml, 2001. http://handle.uws.edu.au:8081/1959.7/622.

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Abstract:

In a multi-server system, probability distributions and loss probabilities for customers arriving with different priority categories are studied. Customers arrive in independent Poisson streams and their service times are exponentially distributed, with different rates for different priorities. The non-queuing customers will be lost if the capacity is fully occupied. In these systems, particularly for higher priority customers, the reduction of the loss probabilities is essential to guarantee the quality of the service. Four different policies for high and low priorities were introduced utilizing the fixed capacity of the system, producing different loss probabilities. The same policies were introduced in the case of a low priority being placed in the queue when the system is fully occupied. An application to the Intensive Care and Coronary Care Unit in Campbelltown Public Hospital in Sydney was introduced. This application analyses the admission and discharge by using queuing theory to develop a model which predicts the proportion of patients from each category that would be prematurely transferred as a function of the size of the unit, number of categories, mean arrival rates, and length of stay.
Master of Science (Hons)

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49

黎文傑 and Man-kit Lai. "Some results on the statistical analysis of directional data." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B31211550.

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50

Szyszkowicz, B. (Barbara) Carleton University Dissertation Mathematics. "Weak convergence of stochastic processes in weighted metrics and their applications to contiguous changepoint analysis." Ottawa, 1992.

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