Department of Mathematics and StatisticsCopyright (c) 2019 Florida International University All rights reserved.
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Recent documents in Department of Mathematics and Statisticsen-usWed, 13 Feb 2019 04:50:58 PST3600Modeling the Influence of Environment and Intervention on Cholera in Haiti
https://digitalcommons.fiu.edu/math_fac/15
https://digitalcommons.fiu.edu/math_fac/15Mon, 11 Feb 2019 08:21:17 PST
We propose a simple model with two infective classes in order to model the cholera epidemic in Haiti. We include the impact of environmental events (rainfall, temperature and tidal range) on the epidemic in the Artibonite and Ouest regions by introducing terms in the transmission rate that vary with environmental conditions. We fit the model on weekly data from the beginning of the epidemic until December 2013, including the vaccination programs that were recently undertaken in the Ouest and Artibonite regions. We then modified these projections excluding vaccination to assess the programs’ effectiveness. Using real-time daily rainfall, we found lag times between precipitation events and new cases that range from 3:4 to 8:4 weeks in Artibonite and 5:1 to 7:4 in Ouest. In addition, it appears that, in the Ouest region, tidal influences play a significant role in the dynamics of the disease. Intervention efforts of all types have reduced case numbers in both regions; however, persistent outbreaks continue. In Ouest, where the population at risk seems particularly besieged and the overall population is larger, vaccination efforts seem to be taking hold more slowly than in Artibonite, where a smaller core population was vaccinated. The models including the vaccination programs predicted that a year and six months later, the mean number of cases in Artibonite would be reduced by about two thousand cases, and in Ouest by twenty four hundred cases below that predicted by the models without vaccination. We also found that vaccination is best when done in the early spring, and as early as possible in the epidemic. Comparing vaccination between the first spring and the second, there is a drop of about 40% in the case reduction due to the vaccine and about 10% per year after that.
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Stephen Tennenbaum et al.On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data
https://digitalcommons.fiu.edu/math_fac/14
https://digitalcommons.fiu.edu/math_fac/14Wed, 29 Mar 2017 10:28:18 PDT
Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.
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Jin Xia et al.On Functions of Several Split-Quaternionic Variables
https://digitalcommons.fiu.edu/math_fac/13
https://digitalcommons.fiu.edu/math_fac/13Mon, 27 Mar 2017 11:18:49 PDT
Alesker studied a relation between the determinant of a quaternionic Hessian of a function and a specific complex volume form. In this note we show that similar relation holds for functions of several split-quaternionic variables and point to some relations with geometry.
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Gueo Grantcharov et al.A Comparison of Some Robust Bicariate Control Charts for Individual Observations
https://digitalcommons.fiu.edu/math_fac/12
https://digitalcommons.fiu.edu/math_fac/12Fri, 24 Mar 2017 17:26:36 PDT
This paper proposed and considered some bivariate control charts to monitor individual observations from a statistical process control. Usual control charts which use mean and variance-covariance estimators are sensitive to outliers. We consider the following robust alternatives to the classical Hoteling’s T2: T2MedMAD, T2MCD, T2MVE A simulation study has been conducted to compare the performance of these control charts. Two real life data are analyzed to illustrate the application of these robust alternatives.
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Moustafa Omar Ahmed Abu Shawiesh et al.A Generalization of Bernoulli's Inequality
https://digitalcommons.fiu.edu/math_fac/11
https://digitalcommons.fiu.edu/math_fac/11Fri, 24 Mar 2017 17:14:51 PDTLaura De Carli et al.On Developing Ridge Regression Parameters: A Graphical investigation
https://digitalcommons.fiu.edu/math_fac/10
https://digitalcommons.fiu.edu/math_fac/10Fri, 27 Jan 2017 09:34:56 PST
In this paper we have reviewed some existing and proposed some new estimators for estimating the ridge parameter k . All in all 19 different estimators have been studied. The investigation has been carried out using Monte Carlo simulations. A large number of different models were investigated where the variance of the random error, the number of variables included in the model, the correlations among the explanatory variables, the sample size and the unknown coefficients vectors b have been varied. For each model we have performed 2000 replications and presented the results both in term of figures and tables. Based on the simulation study, we found that increasing the number of correlated variable, the variance of the random error and increasing the correlation between the independent variables have negative effect on the MSE. When the sample size increases the MSE decreases even when the correlation between the independent variables and the variance of the random error are large. In all situations, the proposed estimators have smaller MSE than the ordinary least squared and some other existing estimators.
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Gisela Muniz et al.A simulation study on some confidence intervals for the population standard deviation
https://digitalcommons.fiu.edu/math_fac/9
https://digitalcommons.fiu.edu/math_fac/9Fri, 27 Jan 2017 09:34:49 PST
In this paper a robust estimator against outliers along with some other existing interval estimators are considered for estimating the population standard deviation. An extensive simulation study has been conducted to compare and evaluate the performance of the interval estimators. The exact and the proposed robust method are easy to calculate and are not overly computer-intensive. It appears that the proposed robust method is performing better than other confidence intervals for estimating the population standard deviation, specifically in the presence of outliers and/or data are from a skewed distribution. Some real-life examples are considered to illustrate the application of the proposed confidence intervals, which also supported the simulation study to some extent.
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Moustafa Omar Ahmed Abu Shawiesh et al.Bayes multiple decision functions
https://digitalcommons.fiu.edu/math_fac/8
https://digitalcommons.fiu.edu/math_fac/8Fri, 27 Jan 2017 09:34:43 PST
This paper deals with the problem of simultaneously making many M binary decisions based on one realization of a random data matrix X. M is typically large and X will usually have M rows associated with each of the M decisions to make, but for each row the data may be low dimensional. Such problems arise in many practical areas such as the biological and medical sciences, where the available dataset is from microarrays or other high-throughput technology and with the goal being to decide which among of many genes are relevant with respect to some phenotype of interest; in the engineering and reliability sciences; in astronomy; in education; and in business. A Bayesian decision-theoretic approach to this problem is implemented with the overall loss function being a cost-weighted linear combination of Type I and Type II loss functions. The class of loss functions considered allows for use of the false discovery rate (FDR), false nondiscovery rate (FNR), and missed discovery rate (MDR) in assessing the quality of decision. Through this Bayesian paradigm, the Bayes multiple decision function (BMDF) is derived and an efficient algorithm to obtain the optimal Bayes action is described. In contrast to many works in the literature where the rows of the matrix X are assumed to be stochastically independent, we allow a dependent data structure with the associations obtained through a class of frailty-induced Archimedean copulas. In particular, non-Gaussian dependent data structure, which is typical with failure-time data, can be entertained. The numerical implementation of the determination of the Bayes optimal action is facilitated through sequential Monte Carlo techniques. The theory developed could also be extended to the problem of multiple hypotheses testing, multiple classification and prediction, and high-dimensional variable selection. The proposed procedure is illustrated for the simple versus simple hypotheses setting and for the composite hypotheses setting through simulation studies. The procedure is also applied to a subset of a microarray data set from a colon cancer study.
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Wensong Wu et al.Using AVL Data to Improve Transit On-Time Performance
https://digitalcommons.fiu.edu/math_fac/7
https://digitalcommons.fiu.edu/math_fac/7Fri, 27 Jan 2017 09:34:36 PST
This paper describes an approach for improving on-time performance at transit agencies. It takes advantage of the schedule adherence information from an AVL system. A methodology that can be used to update the bus timetables by using AVL schedule adherence data is described. Using statistical analysis, the main goal is to maximize the density area of the on-time performance range. From this distribution, the optimal value is obtained and used to update the times in the timetables. Then, a comparison process is used to assess the on-time performance improvements. In addition, a simulation process is presented to provide a different perspective than the statistical methodology. This approach also presents possibilities for further ontime performance improvements. To demonstrate the applicability of this research, a case study using data from Miami-Dade Transit is included. The on-time performance calculations for Routes 99 and 57 also are presented.
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Fabian Cevallos et al.A comparison of some confidence intervals for estimating the population coefficient of variation: a simulation study
https://digitalcommons.fiu.edu/math_fac/6
https://digitalcommons.fiu.edu/math_fac/6Fri, 27 Jan 2017 09:34:29 PST
This paper considers several confidence intervals for estimating the population coefficient of variation based on parametric, nonparametric and modified methods. A simulation study has been conducted to compare the performance of the existing and newly proposed interval estimators. Many intervals were modified in our study by estimating the variance with the median instead of the mean and these modifications were also successful. Data were generated from normal, chi-square, and gamma distributions for CV = 0.1, 0.3, and 0.5. We reported coverage probability and interval length for each estimator. The results were applied to two public health data: child birth weight and cigarette smoking prevalence. Overall, good intervals included an interval for chi-square distributions by McKay (1932), an interval estimator for normal distributions by Miller (1991), and our proposed interval.
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Monika Gulhar et al.Rank and k-nullity of contact manifolds
https://digitalcommons.fiu.edu/math_fac/5
https://digitalcommons.fiu.edu/math_fac/5Fri, 17 Jan 2014 08:14:37 PST
We prove that the dimension of the 1-nullity distribution N(1) on a closed Sasakian manifold M of rankl is at least equal to 2l−1 provided that M has an isolated closed characteristic. The result is then used to provide some examples of k-contact manifolds which are not Sasakian. On a closed, 2n+1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension of N(1) is less than or equal to n+1 or N(1) is the entire tangent bundle TM. In the latter case, the Sasakian manifold Mis isometric to a quotient of the Euclidean sphere under a finite group of isometries. We also point out some interactions between k-nullity, Weinstein conjecture, and minimal unit vector fields.
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Philippe RukimbiraFibrations and contact structures
https://digitalcommons.fiu.edu/math_fac/4
https://digitalcommons.fiu.edu/math_fac/4Thu, 16 Jan 2014 12:43:18 PST
We prove that a closed 3-dimensional manifold is a torus bundle over the circle if and only if it carries a closed nonsingular 1-form which is linearly deformable into contact forms.
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Hamidou Dathe et al.On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data
https://digitalcommons.fiu.edu/math_fac/3
https://digitalcommons.fiu.edu/math_fac/3Thu, 16 Jan 2014 12:30:41 PST
Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.
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Jin Xia et al.Interval and Point Estimators for the Location Parameter of the Three-Parameter Lognormal Distribution
https://digitalcommons.fiu.edu/math_fac/2
https://digitalcommons.fiu.edu/math_fac/2Thu, 16 Jan 2014 10:42:24 PST
The three-parameter lognormal distribution is the extension of the two-parameter lognormal distribution to meet the need of the biological, sociological, and other fields. Numerous research papers have been published for the parameter estimation problems for the lognormal distributions. The inclusion of the location parameter brings in some technical difficulties for the parameter estimation problems, especially for the interval estimation. This paper proposes a method for constructing exact confidence intervals and exact upper confidence limits for the location parameter of the three-parameter lognormal distribution. The point estimation problem is discussed as well. The performance of the point estimator is compared with the maximum likelihood estimator, which is widely used in practice. Simulation result shows that the proposed method is less biased in estimating the location parameter. The large sample size case is discussed in the paper.
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Zhenmin Chen et al.A Modified Resource Distribution Fairness Measure
https://digitalcommons.fiu.edu/math_fac/1
https://digitalcommons.fiu.edu/math_fac/1Wed, 15 Jan 2014 09:39:27 PST
An important issue of resource distribution is the fairness of the distribution. For example, computer network management wishes to distribute network resource fairly to its users. To describe the fairness of the resource distribution, a quantitative fairness score function was proposed in 1984 by Jain et al. The purpose of this paper is to propose a modified network sharing fairness function so that the users can be treated differently according to their priority levels. The mathematical properties are discussed. The proposed fairness score function keeps all the nice properties of and provides better performance when the network users have different priority levels.
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Zhenmin Chen