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Statistical Analysis Of Unreplicated Factorial Designs Using Contrasts, Meixi Yang
Statistical Analysis Of Unreplicated Factorial Designs Using Contrasts, Meixi Yang
Electronic Theses and Dissertations
Factorial designs can have a large number of treatments due to the number of factors and the number of levels of each factor. The number of experimental units required for a researcher to conduct a $k$ factorial experiment is at least the number of treatments. For such an experiment, the total number of experimental units will also depend on the number of replicates for each treatment. The more experimental units used in a study the more the cost to the researcher. The minimum cost is associated with the case in which there is one experimental unit per treatment. That is, …
Generalized Weibull And Inverse Weibull Distributions With Applications, Valeriia Sherina
Generalized Weibull And Inverse Weibull Distributions With Applications, Valeriia Sherina
Electronic Theses and Dissertations
In this thesis, new classes of Weibull and inverse Weibull distributions including the generalized new modified Weibull (GNMW), gamma-generalized inverse Weibull (GGIW), the weighted proportional inverse Weibull (WPIW) and inverse new modified Weibull (INMW) distributions are introduced. The GNMW contains several sub-models including the new modified Weibull (NMW), generalized modified Weibull (GMW), modified Weibull (MW), Weibull (W) and exponential (E) distributions, just to mention a few. The class of WPIW distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Frechet distributions as special cases. Included …
Generalized Classes Of Distributions With Applications To Income And Lifetime Data, Shujiao Huang
Generalized Classes Of Distributions With Applications To Income And Lifetime Data, Shujiao Huang
Electronic Theses and Dissertations
In this thesis, new classes of distributions namely: exponentiated Kumaraswamy-Dagum (EKD), Log-exponentiated Kumaraswamy-Dagum (Log-EKD), McDonald Log-logistic (McLLog) and Gamma-Dagum (GD) distributions are presented. A thorough and comprehensive investigation of these classes of distributions is conducted. Mathematical properties of these classes of distributions including series expansion, hazard and reverse hazard functions, moments, generating functions, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics, moments of order statistics and entropies are presented. Estimation of parameters of these distributions via maximum likelihood technique, Fisher information and asymptotic confidence intervals are given. Maximum likelihood estimation of the parameters of the exponentiated …
An Investigation Of Sensitivity Of An F Test In Locating Change Points In Linear Regression, Jing Sun
An Investigation Of Sensitivity Of An F Test In Locating Change Points In Linear Regression, Jing Sun
Electronic Theses and Dissertations
Change point is a statistic phenomenon, which has many direct applications in climatology, bioinformatics, finance, oceanography and medical imaging. In this thesis, we investigate the sensitivity of the F-test for detecting change points in linear regression, using a two-phase linear regression model. it offers an effective method to detect "undocumented" change points using a form of an F-test. Using simulated data, we explore its sensitivity and accuracy with respect t different parameters in the model.
Comparing K Population Means With No Assumption About The Variances, Tony Yaacoub
Comparing K Population Means With No Assumption About The Variances, Tony Yaacoub
Electronic Theses and Dissertations
In the analysis of most statistically designed experiments, it is common to assume equal variances along with the assumptions that the sample measurements are independent and normally distributed. Under these three assumptions, a likelihood ratio test is used to test for the difference in population means. Typically, the assumption of independence can be justified based on the sampling method used by the researcher. The likelihood ratio test is robust to the assumption of normality. However, the equality of variances is often difficult to justify. It has been found that the assumption of equal variances cannot be made even after transforming …
Exponentially Weighted Moving Average Charts For Monitoring The Process Generalized Variance, Anna Khamitova
Exponentially Weighted Moving Average Charts For Monitoring The Process Generalized Variance, Anna Khamitova
Electronic Theses and Dissertations
The exponentially weighted moving average chart based on the sample generalized variance is studied under the independent multivariate normal model for the vector of quality measurements. The performance of the chart is based on an analysis of the chart's initial and steady-state run length distributions. The three methods that are commonly used to determinate run length distribution, simulation, the integral equation method, and the Markov chain approximation are discussed. The integral equation and Markov chain approaches are analytical methods that require a nu- merical method for determining the probability density and cumulative distribution functions describing the distribution of the sample …