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.
A new family of distribution named Double-Exponential-X family is proposed. The proposed family is generated from the double exponential distribution. The forms of the probability densities and hazard functions of two distinct subfamilies of the proposed family are examined and reported. Generalproperties such as moment, survival, order statistics, probability weighted moments and quartile functions of the models are investigated. A sub family of the developed family of double –Exponential-X family of the distribution known as double-Exponential-Pareto distribution was used to fit a real life data on the use of antiretroviral drugs. Molecular simulation of efficacy of antiretroviral drugs is conducted to evaluate the performance of the
... Show MoreMersing is one of the places that have the potential for wind power development in Malaysia. Researchers often suggest it as an ideal place for generating electricity from wind power. However, before a location is chosen, several factors need to be considered. By analyzing the location ahead of time, resource waste can be avoided and maximum profitability to various parties can be realized. For this study, the focus is to identify the distribution of the wind speed of Mersing and to determine the optimal average of wind speed. This study is critical because the wind speed data for any region has its distribution. It changes daily and by season. Moreover, no determination has been made regarding selecting the average wind speed used for w
... Show MorePorosity and pore structure are important characteristics of pharmaceutical tablets, since they influence the physical properties, such as mechanical strength, density and disintegration time. This paper is an attempt to investigate the pore structure of four different paracetamol tablets based on mercury porosimetry. The intrusion volumes of mercury were used to calculate the pore diameter, pore volume and pore size distribution. The result obtained indicate that the variation of the pore volume in the tablets followed the sequence:- S.D.I. Iraq? Pharmacare,Dubai-U.A.E.? Bron and Burk(UK) London?Lark Laboratories(India), while the variation of surface area followed the sequence:- S.D.I. Iraq? Lark Laboratories(India)? Pharmacare,Dubai-U.A
... Show MoreThe best design of subsurface trickle irrigation systems requires knowledge of water and salt distribution patterns around the emitters that match the root extraction and minimize water losses. The transient distribution of water and salt in a two-dimensional homogeneous Iraqi soil domain under subsurface trickle irrigation with different settings of an emitter is investigated numerically using 2D-HYDRUS software. Three types of Iraqi soil were selected. The effect of altering different values of water application rate and initial soil water content was investigated in the developed model. The coefficient of correlation (R2) and the root-mean-square error (RMSE) was used to validate the predicted numerical res
... 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.
In 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.
The accretion circumstellar disk of young stars and the Brown dwarf plays an essential role in the formation and evaluation of the planet. Our main work in this paper is to investigate the geometrical shape model for the protoplanetary disk around one of the Brown Dwarfs. The photometric measurements for the brown dwarf CFHT-BD-Tau 4 were extracted from the Vizier archive. We used a numerical simulation to build a model of the spectral energy distribution of our target CFHT-BD-Tau 4. The spectral energy distribution model was fitted with observational data for the brown dwarf CFHT-BD-Tau 4. A transitional disk has been assumed around CFHT-BD-Tau 4. We obtained physical properties of the two disks and the size of the gap between them
... Show MoreA 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 MoreThis article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.
In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional dispersion equation. The algorithm for the numerical solution of this equation is based on explicit finite difference approximation. Consistency, conditional stability, and convergence of this numerical method are described. Finally, numerical example is presented to show the dispersion behavior according to the order of the fractional derivative and we demonstrate that our explicit finite difference approximation is a computationally efficient method for solving two-dimensional fractional dispersion equation