1,721,029 research outputs found
Construction of Asymptotic Confidence Ellipse for Pathogen Parameters of Beta-Poisson Dose-Response Model
No full textA Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. x, 89p.Beta-Poisson dose-response model is a popular parametric dose response model
which is extensively applied in Microbial risk area. The advantage of Beta-Poisson
dose-response model is that it is a model which can consider the change in the risk.
The change is possibly happened because of human responses diversity, pathogen
competence diversity, or the interaction between them.
In our project, we divide it by two parts. The rst part is the Theoretical Part. We
will nd we cannot use the Method of Moments and Maximum Likelihood Estimation
directly to create the Con dence Ellipse for simultaneous estimation of Beta-Poisson
dose-response model parameters. Therefore, we need to discover a suitable approximate
distribution function for the Beta-Poisson dose-response model rst. Then, we
will infer the Maximum Likelihood Estimators for the approximation. Afterwards,
we will construct Fisher information matrix. In the nal, we are going to structure a
normal approximation that gives con dence interval for parameters of Beta-Poisson dose-response approximation. The second part is the simulation part. Since we cannot
nd that large number of real pathogen data, we are going to use R programming
to simulate 10; 000 iterations base on 8 groups of the pathogen parameters, such as
the parameters of Shigella spp., S.typhi and so on. Maximum Likelihood Estimates,
and , for parameters will be calculated after the simulation with the sample size
as n = 100; 500, and 1000. As the result of simulation, rst of all, we are going to
calculate errors from the Monte-Carlo estimations. Then, we will use Scatter Plots to
present the sets of parameters, and apply the 95% con dence ellipse from R to check
the approximate model. After that, the Histograms shows the errors of parameters
will be presented for each value of and . Finally, we will summarize the Maximum
Likelihood Estimates of and , For comparing the results of the simulation, we will
calculate the Error of Estimation, the Mean Square Error and the coverage of the
probability. The method is quite useful for the future study in Epidemiology area.Studentye
Performance of Dependent Bootstrap Confidence Intervals For Generalized Gamma Means
No full textA Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. xv, 101 p.In lifetime data analysis (e.g. survival analysis, reliability analysis) the Generalized
Gamma distribution is a versatile lifetime distribution that includes the Exponential,
Gamma, and Weibull distributions as special cases. In such analyses, as with
most statistical analyses, it is often important to gauge the accuracy and precision
of the resulting estimates. One of the most common ways of doing this is by constructing
confidence intervals. Theoretical approaches are not always appropriate in
practice and computational methods are needed. Some of the most common methods
utilize bootstrap sampling procedures.
Through systematic testing, this research looked for general rules of when various
bootstrap methods to confidence interval construction were preferred in the case of
the Generalized Gamma distribution and mean statistic. Specifically, it considered
both the independent (sampling with replacement) and dependent (sampling without
replacement) bootstrap procedures for the following confidence interval methods:
Bootstrap-t; Percentile; and Modified Percentile.
Thousands of samples of Generalized Gamma random variables were generated
(using R version 3.4.2) with different parameter combinations and samples sizes. For
each sample, thousands of bootstrap samples were produced using both the independent
and dependent bootstrap procedures. The original samples and bootstrap
samples were then used to construct the various confidence intervals. Lastly, the
confidence intervals using the same method, parameter combination, and sample size
were analyzed to determine the coverage probability and average length in order to
evaluate the performance.
When only considering coverage probability, the independent bootstrap confidence
interval methods performed well with coverage probabilities close to the confidence
level = 0:90. However, this was achieved with larger average lengths. The dependent
bootstrap procedure was successful as a variance reduction technique compared
to the independent bootstrap procedure by shortening the average length. However,
this was at the cost of lower coverage probabilities.
In the simple case where only the coverage probability is of importance, the preference
should be to use the independent bootstrap, or dependent with a large number
of copies, partnered with the Bootstrap-t or Percentile method (depending on sample
size), rather than the Modified Percentile. When considering both coverage probability
and average length, the Modified Percentile provides more opportunity to strike
a balance between the two performance measures.Studentye
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
An Evaluation of Some Robust Estimators of Regression Coefficients
No full textA Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. vi, 59 p.In the theory of regression analysis, the method of least squares is most commonly
used because of its mathematical beauty and computational simplicity. However, this
method is now criticized more and more because it often has very poor performance
when there are outliers in the data. In this connection a variety of robust statistics are
developed for that they are not unduly a ected by outliers. In this thesis comparison
studies have been made for several robust statistics to see which performs better than
the others. Monte Carlo simulation has been used to carry out the comparison of these
statistics, including the least absolute deviations estimator and the least median of
squares estimator, least trimmed squares estimator and some M-estimators.Studentye
Heavy-Tailed Crack Distribution Families and Applications
No full textA Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. viii, 76 p.The heavy-tailedness and right-skewness are two typical features of loss data
resulting from catastrophic natural phenomena such as severe weather events and
earthquakes. In this thesis, we consider a new class of heavy-tailed crack distribution
families as an extension of the three-parameter Gaussian crack distribution (Volodin
and Dzhungurova, 2000) of which the right tail lacks
exibility to t heavy-tailed
observations.
Several key distributional properties of the generalized crack distribution (Leiva
et al., 2010, Bae and Volodin, 2014) are discussed with a particular emphasis on the
tail behavior. The theoretical tail relationships between the auxiliary distribution
and the resulting crack distribution are studied relying on the classical theories of
extreme values and regular variation. Moreover, we discuss the asymptotic behavior
of the hazard rate function of the generalized crack distribution.
Student's t crack, Laplace crack, the generalized Gaussian crack distributions are
proposed as illustrative examples for theorems and applications. A few model tting exercises are carried out based on both simulated and real catastrophic loss data sets.
For a model tting approach, the maximum likelihood method is used with the pro le
log-likelihood algorithm. The tting results show that the heavy-tailed crack distribution
with an appropriate choice of auxiliary density function outperforms well-known
parametric models, such as Log-normal, Pareto type II and Weibull distributions,
which are popular in modeling positively skewed and heavy-tailed extreme data sets.Studentye
Computational Aspects of An Asymptotic Analysis of Method of Moments Estimators of Parameters For the Binomial Distribution
No full textA Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. xii, 109 p.In this thesis, I evaluate the confidence region of the known parameters p and m of the Binomial distribution and analyze them using descriptive statistics. This research first introduces the method of moments estimators of these parameters, p ̂_n and m ̂_n. Because p ̂_n and m ̂_n do not have mean values and variances, new, modified estimators, p ̃_n and m ̃_n, are presented for the parameters of the binomial distribution. I use the Delta method to develop the asymptotic distribution of p ̂_n, m ̂_n, p ̃_n and m ̃_n. The formulae used to calculate the confidence region are also highlighted in this thesis. These formulae allow us to draw confidence ellipses for the parameters. For the 100(1-α)% confidence region, we consider the ellipses:
{(p,m)|Z ̂_2^2 (p,m)≤χ_2^2 (α)}
and
{(p,m)|Z ̃_2^2 (p,m)≤χ_2^2 (α)},
where χ^2 (α) is the percentile of chi-square distribution with two degrees of freedom. I evaluate the mean areas and standard deviation of areas of ellipses for the method of moments and modified estimators, and the coverage probability of the confidence region. I evaluate the descriptive statistics by examining the coefficients of skewness and kurtosis, and look at the histograms in order to check the quality of the normal approximation of the estimators.Studentye
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