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.
Weibull distribution is considered as one of the most widely distribution applied in real life, Its similar to normal distribution in the way of applications, it's also considered as one of the distributions that can applied in many fields such as industrial engineering to represent replaced and manufacturing time ,weather forecasting, and other scientific uses in reliability studies and survival function in medical and communication engineering fields.
In this paper, The scale parameter has been estimated for weibull distribution using Bayesian method based on Jeffery prior information as a first method , then enhanced by improving Jeffery prior information and then used as a se
... Show More This study includes Estimating scale parameter, location parameter and reliability function for Extreme Value (EXV) distribution by two methods, namely: -
- Maximum Likelihood Method (MLE).
- Probability Weighted Moments Method (PWM).
Used simulations to generate the required samples to estimate the parameters and reliability function of different sizes(n=10,25,50,100) , and give real values for the parameters are and , replicate the simulation experiments (RP=1000)
... Show MoreThe estimation of the stressÙ€ strength reliability of Invers Kumaraswamy distribution will be introduced in this paper based on the maximum likelihood, moment and shrinkage methods. The mean squared error has been used to compare among proposed estimators. Also a Monte Carlo simulation study is conducted to investigate the performance of the proposed methods in this paper.
In this research we been estimated the survival function for data suffer from the disturbances and confusion of Iraq Household Socio-Economic Survey: IHSES II 2012 , to data from a five-year age groups follow the distribution of the Generalized Gamma: GG. It had been used two methods for the purposes of estimating and fitting which is the way the Principle of Maximizing Entropy: POME, and method of booting to nonparametric smoothing function for Kernel, to overcome the mathematical problems plaguing integrals contained in this distribution in particular of the integration of the incomplete gamma function, along with the use of traditional way in which is the Maximum Likelihood: ML. Where the comparison on the basis of the method of the Cen
... Show MoreIn this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of Bayes est
... Show MoreThe fuzzy assignment models (FAMs) have been explored by various literature to access classical values, which are more precise in our real-life accomplishment. The novelty of this paper contributed positively to a unique application of pentagonal fuzzy numbers for the evaluation of FAMs. The new method namely Pascal's triangle graded mean (PT-GM) has presented a new algorithm in accessing the critical path to solve the assignment problems (AP) based on the fuzzy objective function of minimising total cost. The results obtained have been compared to the existing methods such as, the centroid formula (CF) and centroid formula integration (CFI). It has been demonstrated that operational efficiency of this conducted method is exquisitely develo
... Show MoreAbstract. In this work, some new concepts were introduced and the relationship between them was studied. These concepts are filter directed-toward, nano-closure-directed-toward and nano-closure-converge to point, and some theories and results about these concepts were presented. A definition almost-nano-converges for set, almost-nano-cluster-point, and definition of quasi-nano-Hausdorff-closed and was also called nano-Hausdorff-closed relative, were also presented several theories related to these definitions were presented and the relationship between them was studied . We also provided other generalizations, including nano closure continuous mappings and it was also called as nano-weaklycontinuous- mappings, as well as providing a definit
... Show MoreThe main idea of this research is to study fibrewise pairwise soft forms of the more important separation axioms of ordinary bitopology named fibrewise pairwise soft
The Khor Mor gas-condensate processing plant in Iraq is currently facing operational challenges due to foaming issues in the sweetening tower caused by high-soluble hydrocarbon liquids entering the tower. The root cause of the problem could be liquid carry-over as the separation vessels within the plant fail to remove liquid droplets from the gas phase. This study employs Aspen HYSYS v.11 software to investigate the performance of the industrial three-phase horizontal separator, Bravo #2, located upstream of the Khor Mor sweetening tower, under both current and future operational conditions. The simulation results, regarding the size distribution of liquid droplets in the gas product and the efficiency gas/liquid separation, r
... Show More The result of concentration varying of mixture methane with argon and neon gas are believed to study the change in electrons energy distribution function and then the change of the electrons transport parameters including the drift velocity, the mean energy, characteristics energy and diffusion coefficient. In the present work,a contemporary developed computer, simulation program known as Bolsig+ is being used for calculating the electron transport parameters.