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 paper, an algorithm for binary codebook design has been used in vector quantization technique, which is used to improve the acceptability of the absolute moment block truncation coding (AMBTC) method. Vector quantization (VQ) method is used to compress the bitmap (the output proposed from the first method (AMBTC)). In this paper, the binary codebook can be engender for many images depending on randomly chosen to the code vectors from a set of binary images vectors, and this codebook is then used to compress all bitmaps of these images. The chosen of the bitmap of image in order to compress it by using this codebook based on the criterion of the average bitmap replacement error (ABPRE). This paper is suitable to reduce bit rates
... Show MoreFriction Stir Welding (FSW) is one of the most effective solid states joining process and has numerous potential applications in many industries. A FSW numerical tool, based on ANSYS F.E software, has been developed. The amount of the heat gone to the tool dictates the life of the tool and the capability of the tool to produce a good processed zone. Hence, understanding the heat transfer aspect of the friction stir welding is extremely important for improving the process. Many research works were carried out to simulate the friction stir welding using various softwares to determine the temperature distribution for a given set of welding conditions. The objective of this research is to develop a finite element sim
... Show MoreThe present research deal with ecological and geographical distribution of species and genera of Primulaceae in Iraq. The results were revealed that species distributed in the north , north-east and west of Iraq. Anagallis arvensis L. is the most prevalent species tolerant to different environmental conditions, while the species of Primula L. characterized as less widespread and limited in one District. In addition, the districts Rawanduz (MRO) and Sulaymaniyah (MSU) have ranked first in distribution of the species on geographical districts with (75%), while the districts southern desert (DSD) and Basra (LBA) in last place with (16.7%). Maps for geographical distribution for all species were illustrated.
In this research we solved numerically Boltzmann transport equation in order to calculate the transport parameters, such as, drift velocity, W, D/? (ratio of diffusion coefficient to the mobility) and momentum transfer collision frequency ?m, for purpose of determination of magnetic drift velocity WM and magnetic deflection coefficient ? for low energy electrons, that moves in the electric field E, crossed with magnetic field B, i.e; E×B, in the nitrogen, Argon, Helium and it's gases mixtures as a function of: E/N (ratio of electric field strength to the number density of gas), E/P300 (ratio of electric field strength to the gas pressure) and D/? which covered a different ranges for E/P300 at temperatures 300°k (Kelvin). The results show
... Show MoreGroundwater is an essential source because of its high quality and continuous availability characterize this water resource. Therefore, the study of groundwater has required more attention. The present study aims to assess and manage groundwater quality's suitability for various purposes through the Geographical Information System GIS and the Water Quality Index WQI. The study area is located in the city of Baghdad in central Iraq, with an approximate area of 900 , data were collected from the relevant official departments representing the locations of 97 wells of groundwater in the study area for the year 2019, as it included physicochemical parameters such as pH, EC, TDS, Na, K, Mg, Ca, Cl, , and &nbs
... Show MoreIn this paper, we proposed a new class of weighted Rayleigh distribution based on two parameters, scale and shape parameters which are introduced in Rayleigh distribution. The main properties of this class are investigated and derived.
A groundwater quality assessment has been carried out in northeast part of Anbar governorate in western Iraq. We analyzed hydrochemical parameters such as pH, electrical conductivity, total dissolved solids presence of ions to describe groundwater quality. The study area has the only confined aquifer within the geological formation extended in area. Values of groundwater hydrochemical parameters were ranged from (7) to (7.9) for ph, (1599) to (6800) µmhos/cm for electrical conductivity (EC) and (1048) to (4446) mg/l for total dissolved solids (TDS). The origins and types of groundwater in the area were of marine origin and MgCl2 water type while only (6) samples were of continental origin and Na2SO4 wate
... Show MoreThe theory of probabilistic programming may be conceived in several different ways. As a method of programming it analyses the implications of probabilistic variations in the parameter space of linear or nonlinear programming model. The generating mechanism of such probabilistic variations in the economic models may be due to incomplete information about changes in demand, production and technology, specification errors about the econometric relations presumed for different economic agents, uncertainty of various sorts and the consequences of imperfect aggregation or disaggregating of economic variables. In this Research we discuss the probabilistic programming problem when the coefficient bi is random variable
... Show MoreThe approach of the research is to simulate residual chlorine decay through potable water distribution networks of Gukookcity. EPANET software was used for estimating and predicting chlorine concentration at different water network points . Data requiredas program inputs (pipe properties) were taken from the Baghdad Municipality, factors that affect residual chlorine concentrationincluding (pH ,Temperature, pressure ,flow rate) were measured .Twenty five samples were tested from November 2016 to July 2017.The residual chlorine values varied between ( 0.2-2mg/L) , and pH values varied between (7.6 -8.2) and the pressure was very weak inthis region. Statistical analyses were used to evaluated errors. The calculated concentrations by the calib
... Show MoreIn this paper, we investigate the connection between the hierarchical models and the power prior distribution in quantile regression (QReg). Under specific quantile, we develop an expression for the power parameter ( ) to calibrate the power prior distribution for quantile regression to a corresponding hierarchical model. In addition, we estimate the relation between the and the quantile level via hierarchical model. Our proposed methodology is illustrated with real data example.