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 (as done in the first edition 2019). 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. While the revised new chapters have been added (as the current second edition 2024). Chapter six introduces mean vector estimation and covariance matrix estimation. Chapter seven devotes to testing concerning mean: one sample mean, and two sample mean. Chapter eight discusses special case of factorial analysis which is principal components analysis. Chapter nine deals with discriminant analysis. While chapter ten deals with cluster analysis. 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 the readers.
In this research, some robust non-parametric methods were used to estimate the semi-parametric regression model, and then these methods were compared using the MSE comparison criterion, different sample sizes, levels of variance, pollution rates, and three different models were used. These methods are S-LLS S-Estimation -local smoothing, (M-LLS)M- Estimation -local smoothing, (S-NW) S-Estimation-NadaryaWatson Smoothing, and (M-NW) M-Estimation-Nadarya-Watson Smoothing.
The results in the first model proved that the (S-LLS) method was the best in the case of large sample sizes, and small sample sizes showed that the
... Show MoreIn this paper, for the first time we introduce a new four-parameter model called the Gumbel- Pareto distribution by using the T-X method. We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters. Numerical illustration and an application to a real data set are given to show the flexibility and potentiality of the new model.
The paper shows how to estimate the three parameters of the generalized exponential Rayleigh distribution by utilizing the three estimation methods, namely, the moment employing estimation method (MEM), ordinary least squares estimation method (OLSEM), and maximum entropy estimation method (MEEM). The simulation technique is used for all these estimation methods to find the parameters for the generalized exponential Rayleigh distribution. In order to find the best method, we use the mean squares error criterion. Finally, in order to extract the experimental results, one of object oriented programming languages visual basic. net was used
The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the <
... Show MoreThe technology of reducing dimensions and choosing variables are very important topics in statistical analysis to multivariate. When two or more of the predictor variables are linked in the complete or incomplete regression relationships, a problem of multicollinearity are occurred which consist of the breach of one basic assumptions of the ordinary least squares method with incorrect estimates results.
There are several methods proposed to address this problem, including the partial least squares (PLS), used to reduce dimensional regression analysis. By using linear transformations that convert a set of variables associated with a high link to a set of new independent variables and unr
... Show MoreThe use of appropriate and accurate language is of utmost importance when describing people on the move and their dilemma, particularly refugees and displaced persons who have unique legal protection. So, there are a lot of scholars who have investigated the United Nations High Commissioner for Refugees’ (UNHCR) reports, but no one has examined representational and interactional meanings of UNHCR reports. Accordingly, this research aims to explore the role of UNHCR reports in enhancing the value of the humanitarian, which is attributed to the uniqueness of its use of language. The current study investigates the manner in which the textual content interacts with the images that are associated with the category of the UNHCR reports. Four re
... Show MoreThe economical design of plate loaded by pressure can be obtained by using stiffeners instead of increasing the thickness of plate. The main subject of this work is to obtain the effect of stiffener height on the maximum stress in the plate subjected to pressure load. Different plate-stiffener sets are selected to find the effects of stiffener thickness, plate dimensions and pressure, on the optimum stiffener height. The models under consideration are square plates clamped rigidly from four edges. Finite Element method is used to analyze 160 different models by using the Finite Element software package ANSYS version 11. Another analysis method based on maximum stress equation is used to analyze 30 models. The graphical comparison of results
... Show MoreAfamin, which is a human plasma glycoprotein, a putative multifunctional transporter of hydrophobic molecules and a marker for metabolic syndrome. Afamin concentration have been proposed to have a significant role as a predictor of metabolic disorders. Since NAFLD is associated with metabolic risk factors, e.g., dyslipidemia, insulin resistance and visceral obesity, it is considered as the hepatic manifestation of the metabolic syndrome. The objective of this study is to determine Afamin levels in hypothyroid patients with and without fatty liver disease and compare the results with controls. Also to study the relationship of Afamin level with the Anthropometric and Clinical Features (Age, Gender, BMI and Duration of Hypothyroidism) , Serum
... Show MoreStable new derivative (L) Bis[O,O-2,3;O,O-5,6(carboxylic methyliden)]L-ascorbic acid was synthesized in good yield by the reaction of L-ascorbic acid with dichloroacetic acid with ratio (1:2) in presence of potassium hydroxide. The new (L) was characterized by 1H,13C-NMR, elemental analysis (C,H) and Fourier Transform Infrared (FTIR). The complexes of the ligand (L) with metal ion, M+2= (Cu, Co, Ni, Cd and Hg) were synthesized and characterized by FTIR, UV-Visible, Molar conductance, Atomic absorption and the Molar ratio. The analysis evidence showed the binding of the metal ions with (L) through bicarboxylato group manner resulting in six-coordinated metal ion.
In this study, nickel cobaltite (NC) nanoparticles were created using the sol-gel process and used as an adsorbent to adsorb methyl green dye (MG) from aqueous solutions. The adequate preparation of nickel cobaltite nanoparticles was verified using FT-IR, SEM, and X-ray diffraction (XRD) studies. The crystalline particle size of NC nanoparticles was 10.53 nm. The effects of a number of experimental variables, such as temperature, adsorbent dosage, and contact time, were examined. The optimal contact time and adsorbent dosage were 120 minutes and 4.5 mg/L, respectively. Four kinetic models—an intraparticle diffusion, a pseudo-first-order equation, a pseudo-second-order equation, and the Boyd equation—were employed to monitor the adsorpti
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