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.
Iraq depends mainly on Tigris and Euphrates Rivers to provide high percentage of agricultural water use for thousands years. At last years, Iraq is suffering from shortage in water resources due to global climate changes and unfair water politics of the neighboring countries, which affected the future of agriculture plans for irrigation, added to that the lack of developed systems of water management in the irrigation projects and improper allocation of irrigation water, which reduces water use efficiency and lead to losing irrigation water and decreasing in agricultural yield. This study aims at studying the usability of irrigation and leaching scheduling within the irrigating projects and putting a complete annual or seasonal irrigatio
... Show MoreA graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense related. The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). A directed graph is a graph in which edges have orientation. A simple graph is a graph that does not have more than one edge between any two vertices and no edge starts and ends at the same vertex. For a simple undirected graph G with order n, and let denotes its complement. Let δ(G), ∆(G) denotes the minimum degree and maximum degree of G respectively. The complement degree polynomial of G is the polynomial CD[G,x]= , where C
... Show MoreThe charge density distributions (CDD) and the elastic electron
scattering form factors F(q) of the ground state for some even mass
nuclei in the 2s 1d shell ( Ne Mg Si 20 24 28 , , and S 32 ) nuclei have
been calculated based on the use of occupation numbers of the states
and the single particle wave functions of the harmonic oscillator
potential with size parameters chosen to reproduce the observed root
mean square charge radii for all considered nuclei. It is found that
introducing additional parameters, namely 1 , and , 2 which
reflect the difference of the occupation numbers of the states from
the prediction of the simple shell model leads to a remarkable
agreement between the calculated an
The present paper concern with minimax shrinkage estimator technique in order to estimate Burr X distribution shape parameter, when prior information about the real shape obtainable as original estimate while known scale parameter.
Derivation for Bias Ratio, Mean squared error and the Relative Efficiency equations.
Numerical results and conclusions for the expressions mentioned above were displayed. Comparisons for proposed estimator with most recent works were made.
This paper aims to decide the best parameter estimation methods for the parameters of the Gumbel type-I distribution under the type-II censorship scheme. For this purpose, classical and Bayesian parameter estimation procedures are considered. The maximum likelihood estimators are used for the classical parameter estimation procedure. The asymptotic distributions of these estimators are also derived. It is not possible to obtain explicit solutions of Bayesian estimators. Therefore, Markov Chain Monte Carlo, and Lindley techniques are taken into account to estimate the unknown parameters. In Bayesian analysis, it is very important to determine an appropriate combination of a prior distribution and a loss function. Therefore, two different
... Show MoreThe two-neutron halo-nuclei (17B, 11Li, 8He) was investigated using a two-body nucleon density distribution (2BNDD) with two frequency shell model (TFSM). The structure of valence two-neutron of 17B nucleus in a pure (1d5/2) state and in a pure (1p1/2) state for 11L and 8He nuclei. For our tested nucleus, an efficient (2BNDD's) operator for point nucleon system folded with two-body correlation operator's functions was used to investigate nuclear matter density distributions, root-mean square (rms) radii, and elastic electron scattering form factors. In the nucleon-nucleon forces the correlation took account of
... Show MoreIn this paper, the reliability and scheduling of maintenance of some medical devices were estimated by one variable, the time variable (failure times) on the assumption that the time variable for all devices has the same distribution as (Weibull distribution.
The method of estimating the distribution parameters for each device was the OLS method.
The main objective of this research is to determine the optimal time for preventive maintenance of medical devices. Two methods were adopted to estimate the optimal time of preventive maintenance. The first method depends on the maintenance schedule by relying on information on the cost of maintenance and the cost of stopping work and acc
... Show MoreThe location of fire brigade stations and equipment has a significant impact on the efficacy and efficiency of fire brigade department services. The challenge addressed by this study was that the fire brigade department required a consistent and repeatable technique to assess the response capabilities and safeguarding levels offered as the city of Samawah/Iraq grew and changed. Evaluating the locations of the current fire brigade stations in the city of Samawah is the aspect addressed by the research to determine the accuracy and validity of the locations of these stations by the competent authorities and their suitability to the area of the city’s neighborhoods and its residents. The Iraqi Ministry of Housing, Construction, Municipalitie
... Show More In this paper the research represents an attempt of expansion in using the parametric and non-parametric estimators to estimate the median effective dose ( ED50 ) in the quintal bioassay and comparing between these methods . We have Chosen three estimators for Comparison. The first estimator is
( Spearman-Karber ) and the second estimator is ( Moving Average ) and The Third estimator is ( Extreme Effective Dose ) . We used a minimize Chi-square as a parametric method. We made a Comparison for these estimators by calculating the mean square error of (ED50) for each one of them and comparing it with the optimal the mean square
Truncated distributions arise naturally in many practical situations. It’s a conditional distribution that develops when the parent distribution's domain is constrained to a smaller area. The distribution of a right truncated is one of the types of a single truncated that is restricted within a specific field and usually occurs when the specified period for the study is complete. Hence, this paper introduces Right Truncated Inverse Generalized Rayleigh Distribution (RTIGRD) with two parameters is introduced. Then, provided some properties such as; (probability density function, cumulative distribution function (CDF), survival function, hazard function, rth moment, mean, variance, Moment Generating Function, Skewness, kurtosi
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