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 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 MoreFresh water resources in terms of water quality is a crucial issue worldwide. In Egypt, the Nile River is the main source of fresh water in the country and monitoring its water quality is a major task on governments and research levels. In the present case study, the physical, chemical and algal distribution in Nile River was monitored over two seasons (winter and summer) in 2019. The aims of the study were to check the seasonal variation among the different water parameters and also to check the correlations between those parameters. Water samples were collected from the Nile in Cairo governorate in EGYPT. The different physiochemical and microbiological properties in water samples were assessed. The studied parameters were included: te
... Show MoreIn recent years, the number of applications utilizing mobile wireless sensor networks (WSNs) has increased, with the intent of localization for the purposes of monitoring and obtaining data from hazardous areas. Location of the event is very critical in WSN, as sensing data is almost meaningless without the location information. In this paper, two Monte Carlo based localization schemes termed MCL and MSL* are studied. MCL obtains its location through anchor nodes whereas MSL* uses both anchor nodes and normal nodes. The use of normal nodes would increase accuracy and reduce dependency on anchor nodes, but increases communication costs. For this reason, we introduce a new approach called low communication cost schemes to reduce communication
... Show MoreThis paper is specifically a detailed review of the Spatial Quantile Autoregressive (SARQR) model that refers to the incorporation of quantile regression models into spatial autoregressive models to facilitate an improved analysis of the characteristics of spatially dependent data. The relevance of SARQR is emphasized in most applications, including but not limited to the fields that might need the study of spatial variation and dependencies. In particular, it looks at literature dated from 1971 and 2024 and shows the extent to which SARQR had already been applied previously in other disciplines such as economics, real estate, environmental science, and epidemiology. Accordingly, evidence indicates SARQR has numerous benefits compar
... Show MoreThis paper is specifically a detailed review of the Spatial Quantile Autoregressive (SARQR) model that refers to the incorporation of quantile regression models into spatial autoregressive models to facilitate an improved analysis of the characteristics of spatially dependent data. The relevance of SARQR is emphasized in most applications, including but not limited to the fields that might need the study of spatial variation and dependencies. In particular, it looks at literature dated from 1971 and 2024 and shows the extent to which SARQR had already been applied previously in other disciplines such as economics, real estate, environmental science, and epidemiology. Accordingly, evidence indicates SARQR has numerous benefits compar
... Show MoreThere is a great operational risk to control the day-to-day management in water treatment plants, so water companies are looking for solutions to predict how the treatment processes may be improved due to the increased pressure to remain competitive. This study focused on the mathematical modeling of water treatment processes with the primary motivation to provide tools that can be used to predict the performance of the treatment to enable better control of uncertainty and risk. This research included choosing the most important variables affecting quality standards using the correlation test. According to this test, it was found that the important parameters of raw water: Total Hardn
The demand for single photon sources in quantum key distribution (QKD) systems has necessitated the use of weak coherent pulses (WCPs) characterized by a Poissonian distribution. Ensuring security against eavesdropping attacks requires keeping the mean photon number (µ) small and known to legitimate partners. However, accurately determining µ poses challenges due to discrepancies between theoretical calculations and practical implementation. This paper introduces two experiments. The first experiment involves theoretical calculations of µ using several filters to generate the WCPs. The second experiment utilizes a variable attenuator to generate the WCPs, and the value of µ was estimated from the photons detected by the BB
... Show MoreThis research deals with the use of a number of statistical methods, such as the kernel method, watershed, histogram, and cubic spline, to improve the contrast of digital images. The results obtained according to the RSME and NCC standards have proven that the spline method is the most accurate in the results compared to other statistical methods.
Grey system theory is a multidisciplinary scientific approach, which deals with systems that have partially unknown information (small sample and uncertain information). Grey modeling as an important component of such theory gives successful results with limited amount of data. Grey Models are divided into two types; univariate and multivariate grey models. The univariate grey model with one order derivative equation GM (1,1) is the base stone of the theory, it is considered the time series prediction model but it doesn’t take the relative factors in account. The traditional multivariate grey models GM(1,M) takes those factor in account but it has a complex structure and some defects in " modeling mechanism", "parameter estimation "and "m
... Show More