Mathematics Commons^™

Copula-Based Zero-Inflated Count Time Series Models, Mohammed Sulaiman Alqawba

Mathematics & Statistics Theses & Dissertations

Count time series data are observed in several applied disciplines such as in environmental science, biostatistics, economics, public health, and finance. In some cases, a specific count, say zero, may occur more often than usual. Additionally, serial dependence might be found among these counts if they are recorded over time. Overlooking the frequent occurrence of zeros and the serial dependence could lead to false inference. In this dissertation, we propose two classes of copula-based time series models for zero-inflated counts with the presence of covariates. Zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and zero-inflated Conway-Maxwell-Poisson (ZICMP) distributed marginals of the …

Semi-Parametric Likelihood Functions For Bivariate Survival Data, S. H. Sathish Indika

Mathematics & Statistics Theses & Dissertations

Because of the numerous applications, characterization of multivariate survival distributions is still a growing area of research. The aim of this thesis is to investigate a joint probability distribution that can be derived for modeling nonnegative related random variables. We restrict the marginals to a specified lifetime distribution, while proposing a linear relationship between them with an unknown (error) random variable that we completely characterize. The distributions are all of positive supports, but one class has a positive probability of simultaneous occurrence. In that sense, we capture the absolutely continuous case, and the Marshall-Olkin type with a positive probability of …

Rao's Quadratic Entropy And Some New Applications, Yueqin Zhao

Mathematics & Statistics Theses & Dissertations

Many problems in statistical inference are formulated as testing the diversity of populations. The entropy functions measure the similarity of a distribution function to the uniform distribution and hence can be used as a measure of diversity. Rao (1982a) proposed the concept of quadratic entropy. Its concavity property makes the decomposition similar to ANOVA for categorical data feasible. In this thesis, after reviewing the properties and providing a modification to quadratic entropy, various applications of quadratic entropy are explored. First, analysis of quadratic entropy with the suggested modification to analyze the contingency table data is explored. Then its application to …

Analysis Of Models For Longitudinal And Clustered Binary Data, Weiming Yang

Mathematics & Statistics Theses & Dissertations

This dissertation deals with modeling and statistical analysis of longitudinal and clustered binary data. Such data consists of observations on a dichotomous response variable generated from multiple time or cluster points, that exhibit either decaying correlation or equi-correlated dependence. The current literature addresses modeling the dependence using an appropriate correlation structure, but ignores the feasible bounds on the correlation parameter imposed by the marginal means.

The first part of this dissertation deals with two multivariate probability models, the first order Markov chain model and the multivariate probit model, that adhere to the feasible bounds on the correlation. For both the …

Statistical Analysis Of Longitudinal And Multivariate Discrete Data, Deepak Mav

Mathematics & Statistics Theses & Dissertations

Correlated multivariate Poisson and binary variables occur naturally in medical, biological and epidemiological longitudinal studies. Modeling and simulating such variables is difficult because the correlations are restricted by the marginal means via Fréchet bounds in a complicated way. In this dissertation we will first discuss partially specified models and methods for estimating the regression and correlation parameters. We derive the asymptotic distributions of these parameter estimates. Using simulations based on extensions of the algorithm due to Sim (1993, Journal of Statistical Computation and Simulation, 47, pp. 1–10), we study the performance of these estimates using infeasibility, coverage probabilities of the …

Nearly Balanced And Resolvable Block Designs, Brian Henry Reck

Mathematics & Statistics Theses & Dissertations

One of the fundamental principles of experimental design is the separation of heterogeneous experimental units into subsets of more homogeneous units or blocks in order to isolate identifiable, unwanted, but unavoidable, variation in measurements made from the units. Given v treatments to compare, and having available b blocks of k experimental units each, the thoughtful statistician asks, “What is the optimal allocation of the treatments to the units?” This is the basic block design problem. Let n_ij be the number of times treatment i is used in block j and let N be the v x b matrix N …

Analysis Of Repeated Measures Data Under Circular Covariance, Andrew Montgomery Hartley

Mathematics & Statistics Theses & Dissertations

Circular covariance is important in modelling phenomena in epidemiological, communications and numerous physical contexts. We introduce and develop a variety of methods which make it a more versatile tool. First, we present two classes of estimators for use in the presence of missing observations. Using simulations, we show that the mean squared errors of the estimators of one of these classes are smaller than those of the Maximum Likelihood (ML) estimators under certain conditions. Next, we propose and discuss a parsimonious, autoregressive type of circular covariance structure which involves only two parameters. We specify ML and other types of estimators …

Some Sampling Designs And Estimation Problems, Hassan Lakkis

Mathematics & Statistics Theses & Dissertations

In the first chapter we review some standard estimators in sampling from a finite population, and some design-based estimators in sampling from a continuous universe.

In concert with the theory initiated by professor Douglas Robson (personal communication) and later presented by Cordy (1993), we consider design-based variance estimation for probability sampling from a continuous and spatially distributed universe. Using this theory in chapter two, the sampling design of one random point from each cell of a translated grid is investigated and the problem of edge effects on estimation is illustrated with examples. Also in chapter four, standard systematic sampling methods …

Estimation In A Marked Poisson Error Recapture Model Of Software Reliability, Rajan Gupta

Mathematics & Statistics Theses & Dissertations

Nayak's (1988) model for the detection, removal, and recapture of the errors in a computer program is extended to a larger family of models in which the probabilities that the successive programs produce errors are described by the tail probabilities of discrete distribution on the positive integers. Confidence limits are derived for the probability that the final program produces errors. A comparison of the asymptotic variances of parameter estimates given by the error recapture and by the repetitive-run procedure of Nagel, Scholz, and Skrivan (1982) is made to determine which of these procedures efficiently uses the test time.

Estimation In Truncated Exponential Family Of Distributions, Laxman M. Hegde

Mathematics & Statistics Theses & Dissertations

Estimating the parameters of a truncated distribution is a well known problem in statistical inference. The non-existence of the maximum likelihood estimator (m.l.e.) with positive probability in certain truncated distributions is not well known. To mention a few results in the literature:

(i) Deemer and Votaw 1955 show that the maximum likelihood estimator does not exist in a truncated negative exponential distribution on 0,T , T > 0 known, whenever the sample mean x (GREATERTHEQ) T/2.

(ii) Broeder 1955 shows that the maximum likelihood estimator of the scale parameter of a truncated gamma distribution, with the shape parameter being known, becomes …