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.
The monthly time series of the Total Suspended Solids (TSS) concentrations in Euphrates River at Nasria was analyzed as a time series. The data used for the analysis was the monthly series during (1977-2000).
The series was tested for nonhomogenity and found to be nonhomogeneous. A significant positive jump was observed after 1988. This nonhomogenity was removed using a method suggested by Yevichevich (7). The homogeneous series was then normalized using Box and Cox (2) transformation. The periodic component of the series was fitted using harmonic analyses, and removed from the series to obtain the dependent stochastic component. This component was then modeled using first order autoregressive model (Markovian chain). The above a
... Show MoreGenerally fossil based fuels are used in internal combustion engines as an energy source.
Excessive use of fossil based fuels diminishes present reserves and increases the air pollution in
urban areas. This enhances the importance of the effective use of present reserves and/or to develop
new alternative fuels, which are environment friendly. Use of alternative fuel is a way of emission
control. The term “Alternative Gaseous Fuels” relates to a wide range of fuels that are in the
gaseous state at ambient conditions, whether when used on their own or as components of mixtures
with other fuels.
In this study, a single cylinder diesel engine was modified to use LPG in dual fuel mode to study
the performance, emis
A Raman spectroscopy method was optimised to examine the chemical changes of aspirin tablets after interaction with helium temperatures. Several aspirin tablets were exposed to plasma-assisted desorption ionisation flame for different times (10, 30, 50, 60, 180 and 300s) and then analysed by Raman spectroscopy using optimal conditions. The changes in chemistry between exposed and fresh (without exposure to plasma) tablets were compared. The vibrational peaks of the aspirin molecule in the Raman spectrum were identified by checking the peak position. The results showed clear spectra with increases in intensity of vibrational peaks until 30s, whereas no spectra were measured for the exposed tablets to plasma flame after 50s. It can, the
... Show MoreThe accurate determination of nuclear radius is fundamental to understanding nuclear structure and interactions. The present study conducts a comprehensive theoretical analysis of nuclear radius measurements using various nuclear structure models, including the empirical mass-number scaling model, the Hartree-Fock approach, and the relativistic mean-field (RMF) theory. These models are systematically compared against experimental nuclear radii to evaluate their predictive accuracy and assess their strengths and limitations. The study also incorporates an uncertainty analysis to quantify the reliability of theoretical predictions, employing Monte Carlo simulations and Bayesian inference techniques to refine estimations. The results r
... Show MoreThe earth-air heat exchanger (EHX) has a promising potential to passively save the energy consumption of traditional air conditioning systems while maintaining a high degree of indoor comfort. The use of EHX systems for air conditioning in commercial and industrial settings offers several environmental benefits and is capable of operating in both standalone and hybrid modes. This study tests the performance and effectiveness of an EHX design in a sandy soil area in Baghdad, Iraq. The area has a climate of the subtropical semi-humid type. Ambient air temperatures and soil temperatures were recorded throughout the months of 2021. During the months of January and June, the temperatures of the inlet and outflow air at varying air veloci
... Show MoreThe reservoir characterization and rock typing is a significant tool in performance and prediction of the reservoirs and understanding reservoir architecture, the present work is reservoir characterization and quality Analysis of Carbonate Rock-Types, Yamama carbonate reservoir within southern Iraq has been chosen. Yamama Formation has been affected by different digenesis processes, which impacted on the reservoir quality, where high positively affected were: dissolution and fractures have been improving porosity and permeability, and destructive affected were cementation and compaction, destroyed the porosity and permeability. Depositional reservoir rock types characterization has been identified de
The performance in the 110-meter hurdles at the sprint hurdles event is determined by several physical and physiological qualities. Nonetheless, relatively little attention has been paid to the predictability of such factors in determining race performance. This study seeks to fill this gap by establishing the most critical physical and physiological characteristics affecting elite hurdlers’ performance and creating a statistical model that predicts race times from the identified measurable characteristics. The study utilized a descriptive research design in-volving six elite male hurdlers, all of whom completed a battery of standardized physical and functional tests to assess their explosive lower-body strength, agility, reaction
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