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Full-Text Articles in Probability
Supervised Classification Using Copula And Mixture Copula, Sumen Sen
Supervised Classification Using Copula And Mixture Copula, Sumen Sen
Mathematics & Statistics Theses & Dissertations
Statistical classification is a field of study that has developed significantly after 1960's. This research has a vast area of applications. For example, pattern recognition has been proposed for automatic character recognition, medical diagnostic and most recently in data mining. Classical discrimination rule assumes normality. However in many situations, this assumption is often questionable. In fact for some data, the pattern vector is a mixture of discrete and continuous random variables. In this dissertation, we use copula densities to model class conditional distributions. Such types of densities are useful when the marginal densities of a pattern vector are not normally …
Modeling And Efficient Estimation Of Intra-Family Correlations, Roy Sabo
Modeling And Efficient Estimation Of Intra-Family Correlations, Roy Sabo
Mathematics & Statistics Theses & Dissertations
Familial data occur when observations are taken on multiple members of the same family. Due to relationships between these members, both genetic and by cohabitation, their response variables will likely exhibit some form of dependence. Most of the existing literature models this dependence with an equicorrelated structure. This structure is appropriate when the dependencies between family members are similar, such as in genetic studies, but not in cases where we expect the dependencies to differ, such as behavioral comparisons across different age groups. In this dissertation we first discuss an alternative structure based upon first-order autoregressive correlation. Specifically we create …
Estimation In A Marked Poisson Error Recapture Model Of Software Reliability, Rajan Gupta
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.
Large Deviation Local Limit Theorems For Ratio Statistics, Sanjeev V. Sabnis
Large Deviation Local Limit Theorems For Ratio Statistics, Sanjeev V. Sabnis
Mathematics & Statistics Theses & Dissertations
Let {T„, n > 1} be an arbitrary sequence of non-lattice random variables and {Sn, n > 1} be another sequence of positive non-lattice random variables. Let the two sequences be independent. Let Ø1n and Ø2n be the moment genereating functions of {Tn, n > 1} and { Sn,n > 1} respectively. Let {an} be a sequence of real numbers such that an —»• oo.