This Book is intended to be textbook studied for undergraduate course in multivariate analysis. This book is designed to be used in semester system. In order to achieve the goals of the book, it is divided into the following chapters. Chapter One introduces matrix algebra. Chapter Two devotes to Linear Equation System Solution with quadratic forms, Characteristic roots & vectors. Chapter Three discusses Partitioned Matrices and how to get Inverse, Jacobi and Hessian matrices. Chapter Four deals with Multivariate Normal Distribution (MVN). Chapter Five concern with Joint, Marginal and Conditional Normal Distribution, independency and correlations. Many solved examples are intended in this book, in addition to a variety of unsolved relied problems at the end of each chapter to enrich the statistical knowledge of our students.
Room temperature ionic liquids show potential as an alternative to conventional organic membrane solvents mainly due to their properties of low vapour pressure, low volatility and they are often stable. In the present work, the technical feasibilities of room temperature ionic liquids as bulk liquid membranes for phenol removal were investigated experimentally. In this research several hydrophobic ionic liquids were synthesized at laboratory. These ionic liquids include (1-butyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide[Bmim][NTf2], 1-Hexyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide[Hmim][NTf2], 1-octyl-3-methylimidazolium bis (trifluoromethylsulfonyl)imide[Omim][NTf2],1‐butyl
... Show MoreInferential methods of statistical distributions have reached a high level of interest in recent years. However, in real life, data can follow more than one distribution, and then mixture models must be fitted to such data. One of which is a finite mixture of Rayleigh distribution that is widely used in modelling lifetime data in many fields, such as medicine, agriculture and engineering. In this paper, we proposed a new Bayesian frameworks by assuming conjugate priors for the square of the component parameters. We used this prior distribution in the classical Bayesian, Metropolis-hasting (MH) and Gibbs sampler methods. The performance of these techniques were assessed by conducting data which was generated from two and three-component mixt
... Show MoreIn this paper, some estimators for the unknown shape parameter and reliability function of Basic Gompertz distribution have been obtained, such as Maximum likelihood estimator and Bayesian estimators under Precautionary loss function using Gamma prior and Jefferys prior. Monte-Carlo simulation is conducted to compare mean squared errors (MSE) for all these estimators for the shape parameter and integrated mean squared error (IMSE's) for comparing the performance of the Reliability estimators. Finally, the discussion is provided to illustrate the results that summarized in tables.
The effect of short range correlations on the inelastic longitudinal
Coulomb form factors for different states of J 4 , T 1with
excitation energies 3.553,7.114, 8.960 and 10.310 MeV in 18O is
analyzed. This effect (which depends on the correlation parameter )
is inserted into the ground state charge density distribution through
the Jastrow type correlation function. The single particle harmonic
oscillator wave function is used with an oscillator size parameter b.
The parameters and b are considered as free parameters, adjusted
for each excited state separately so as to reproduce the experimental
root mean square charge radius of 18O. The model space of 18O does
not contribute to the tra
In this paper, we used the maximum likelihood estimation method to find the estimation values ​​for survival and hazard rate functions of the Exponential Rayleigh distribution based on a sample of the real data for lung cancer and stomach cancer obtained from the Iraqi Ministry of Health and Environment, Department of Medical City, Tumor Teaching Hospital, depending on patients' diagnosis records and number of days the patient remains in the hospital until his death.
In the current study, the researchers have been obtained Bayes estimators for the shape and scale parameters of Gamma distribution under the precautionary loss function, assuming the priors, represented by Gamma and Exponential priors for the shape and scale parameters respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation.
Based on Monte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s). The results show that, the performance of Bayes estimator under precautionary loss function with Gamma and Exponential priors is better than other estimates in all cases.
We are used Bayes estimators for unknown scale parameter when shape Parameter is known of Erlang distribution. Assuming different informative priors for unknown scale parameter. We derived The posterior density with posterior mean and posterior variance using different informative priors for unknown scale parameter which are the inverse exponential distribution, the inverse chi-square distribution, the inverse Gamma distribution, and the standard Levy distribution as prior. And we derived Bayes estimators based on the general entropy loss function (GELF) is used the Simulation method to obtain the results. we generated different cases for the parameters of the Erlang model, for different sample sizes. The estimates have been comp
... Show MoreThe Log-Logistic distribution is one of the important statistical distributions as it can be applied in many fields and biological experiments and other experiments, and its importance comes from the importance of determining the survival function of those experiments. The research will be summarized in making a comparison between the method of maximum likelihood and the method of least squares and the method of weighted least squares to estimate the parameters and survival function of the log-logistic distribution using the comparison criteria MSE, MAPE, IMSE, and this research was applied to real data for breast cancer patients. The results showed that the method of Maximum likelihood best in the case of estimating the paramete
... Show MoreForward-swept wings were researched and introduced to improve maneuverability, control, and fuel efficiency while reducing drag and they are often used alongside canards, to further enhance their characteristics. In this research, the effects of canard dihedral angles on the wing loading of a forward-swept wing in transonic flow conditions were studied, as the wing loading provides a measure of wing’s efficiency (lift/drag). A generic aircraft model from literatures was selected, simulated, and compared to, using CFD software ANSYS/Fluent where the flow equations were solved to calculate the aerodynamic characteristics. The research was carried at two different Mach numbers, 0.6 and 0.9, for five different canard dihedral angles which tra
... Show MoreThe main idea of this research is to consider fibrewise pairwise versions of the more important separation axioms of ordinary bitopology named fibrewise pairwise - spaces, fibrewise pairwise - spaces, fibrewise pairwise - spaces, fibrewise pairwise -Hausdorff spaces, fibrewise pairwise functionally -Hausdorff spaces, fibrewise pairwise -regular spaces, fibrewise pairwise completely -regular spaces, fibrewise pairwise -normal spaces and fibrewise pairwise functionally -normal spaces. In addition we offer some results concerning it.