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 objective of this study was tointroduce a recursive least squares (RLS) parameter estimatorenhanced by using a neural network (NN) to facilitate the computing of a bit error rate (BER) (error reduction) during channels estimation of a multiple input-multiple output orthogonal frequency division multiplexing (MIMO-OFDM) system over a Rayleigh multipath fading channel.Recursive least square is an efficient approach to neural network training:first, the neural network estimator learns to adapt to the channel variations then it estimates the channel frequency response. Simulation results show that the proposed method has better performance compared to the conventional methods least square (LS) and the original RLS and it is more robust a
... Show MoreChannel estimation (CE) is essential for wireless links but becomes progressively onerous as Fifth Generation (5G) Multi-Input Multi-Output (MIMO) systems and extensive fading expand the search space and increase latency. This study redefines CE support as the process of learning to deduce channel type and signal-tonoise ratio (SNR) directly from per-tone Orthogonal Frequency-Division Multiplexing (OFDM) observations,with blind channel state information (CSI). We trained a dual deep model that combined Convolutional Neural Networks (CNNs) with Bidirectional Recurrent Neural Networks (BRNNs). We used a lookup table (LUT) label for channel type (class indices instead of per-tap values) and ordinal supervision for SNR (0–20 dB,5-dB steps). T
... Show MoreDiazotization reaction between 1-(2,4,6-trihydroxy-phenyl)-ethanone and diazonium salts produced the ligand 4-(3-Acetyl-2,4,6-trihydroxy-phenylazo)-N-(5-methyl-isoxazol-3-yl)- benzenesulfonamide, which in turn reacted with the metal ions (Ni2+, Zn2+, Pd2+ and Pt4+) forming stable complexes with Octahedral geometry suggest of (Ni2+ and Pt4+), Zn2+ complex Tetrahedral and Pd2+ complex Square planer. The creation of such complexes was detected by employing spectroscopic means involving ultraviolet-visible, which proved the obtained geometries; FT-IR confirmed the formation of the azo group and the coordination with metal ions through it. Thermogravimetric analysis studies demonstrated the coordination of water residues (aqua or hydrate) with m
... Show MoreThe mucilage was isolated from mustard seeds and identification by some different methods like, thermo gravimetric, FTlR., X-ray powdered, proton NMR, FTIR spectra of the three gums contain different functional group in the gums, major peaks bands noticed were belong to OH (3410.15 – 3010.88) group from hydroxyl group, CH aliphatic (2925-2343.51), C-O (1072.42-1060.85) group and C=O 1743.65, Thermo chemical parameters of mucilage was evaluated and compared with the standard gums, Results indicated the mucilage was decomposed in 392°C and mass loss 55%, The X ray process found the mucilage had single not sharp peak
... Show MoreIn this paper, Response Surface Method (RSM) is utilized to carry out an investigation of the impact of input parameters: electrode type (E.T.) [Gr, Cu and CuW], pulse duration of current (Ip), pulse duration on time (Ton), and pulse duration off time (Toff) on the surface finish in EDM operation. To approximate and concentrate the suggested second- order regression model is generally accepted for Surface Roughness Ra, a Central Composite Design (CCD) is utilized for evaluating the model constant coefficients of the input parameters on Surface Roughness (Ra). Examinations were performed on AISI D2 tool steel. The important coefficients are gotten by achieving successfully an Analysis of V
... Show MoreTwo Schiff bases, namely, 3-(benzylidene amino) -2-thioxo-6-methyl 2,5-dihydropyrimidine-4(3H)-one (LS])and 3-(benzylidene amino)-6-methyl pyrimidine 4(3H, 5H)-dione(LA)as chelating ligands), were used to prepare some complexes of Cr(III), La(III), and Ce(III)] ions. Standard physico-chemical procedures including metal analysis M%, element microanalysis (C.H.N.S) , magnetic susceptibility, conductometric measurements, FT-IR and UV-visible Spectra were used to identify Metal (III) complexes and Schiff bases (LS) and (LA). According to findings, a [Cr(III) complex] showed six coordinated octahedral geometry, while [La(III), and Ce(III) complexes]were structured with coordination number seven. Schiff's bases a
... Show MoreThis paper presents a comprehensive numerical analysis of the improvement in bearing capacity and settlement performance of hexagonal shallow footings with inclined skirts. Various numerical analyses were conducted using PLAXIS 3D to investigate the influence of skirt length-to-footing width (L/B) ratios and skirt inclination angles (θ) on hexagonal footings in loose sand. The models showed very good agreement with experimental data reported in previous studies, with an R² value of 0.996 and a maximum error of less than 4.31%. It was concluded that the inclusion of inclined skirts has a positive effect on bearing capacity, increasing it by up to approximately 2.97 times compared to non-inclined configurations, while significantly
... Show MoreThe Weibull distribution is considered one of the Type-I Generalized Extreme Value (GEV) distribution, and it plays a crucial role in modeling extreme events in various fields, such as hydrology, finance, and environmental sciences. Bayesian methods play a strong, decisive role in estimating the parameters of the GEV distribution due to their ability to incorporate prior knowledge and handle small sample sizes effectively. In this research, we compare several shrinkage Bayesian estimation methods based on the squared error and the linear exponential loss functions. They were adopted and compared by the Monte Carlo simulation method. The performance of these methods is assessed based on their accuracy and computational efficiency in estimati
... Show MoreIn this paper the use of a circular array antenna with adaptive system in conjunction with modified Linearly Constrained Minimum Variance Beam forming (LCMVB) algorithm is proposed to meet the requirement of Angle of Arrival (AOA) estimation in 2-D as well as the Signal to Noise Ratio (SNR) of estimated sources (Three Dimensional 3-D estimation), rather than interference cancelation as it is used for. The proposed system was simulated, tested and compared with the modified Multiple Signal Classification (MUSIC) technique for 2-D estimation. The results show the system has exhibited astonishing results for simultaneously estimating 3-D parameters with accuracy approximately equivalent to the MUSIC technique (for estimating elevation and a
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