This Book is the second edition that intended to be textbook studied for undergraduate/ postgraduate course in mathematical statistics. In order to achieve the goals of the book, it is divided into the following chapters. Chapter One introduces events and probability review. Chapter Two devotes to random variables in their two types: discrete and continuous with definitions of probability mass function, probability density function and cumulative distribution function as well. Chapter Three discusses mathematical expectation with its special types such as: moments, moment generating function and other related topics. Chapter Four deals with some special discrete distributions: (Discrete Uniform, Bernoulli, Binomial, Poisson, Geometric, Negative Binomial and Hypergeometric) with their mathematical formulas of p.m.f., C.D.F. and m.g.f. Chapter Five deals with some special continuous distributions: (Uniform, Normal, Exponential, Gamma and Beta) with their mathematical formulas of p.m.f., C.D.F. and m.g.f. Many solved examples are intended in this book (obtaining mean and variance of distributions by m.g.f.). Chapter Six introduces univariate discrete and continuous transformations, i.e., one dimensional variables and their yielding probability distributions. Chapter Seven devotes to truncation of distributions from left, right or both sides, beside the probability distribution of order statistics. Chapter Eight discusses mathematical features of joint, marginal and conditional distributions, as well as independency via covariance and correlation of bivariate distributions. Chapter Nine deals with some special topics such as getting distribution for some transformation from multidimensional random variables by using moment generating function (m.g.f.) and cumulative distribution function (C.D.F.) Many solved examples (about 100) are intended in this book, in addition to a variety of unsolved relied problems (about 150) at the end of each chapter to enrich the statistical knowledge of our readers.
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 class of quasi semi -convex functions and pseudo semi -convex functions are presented in this paper by combining the class of -convex functions with the class of quasi semi -convex functions and pseudo semi -convex functions, respectively. Various non-trivial examples are introduced to illustrate the new functions and show their relationships with -convex functions recently introduced in the literature. Different general properties and characteristics of this class of functions are established. In addition, some optimality properties of generalized non-linear optimization problems are discussed. In this generalized optimization problems, we used, as the objective function, quasi semi -convex (respectively, strictly quasi semi -convex
... Show MoreIn this study we focused on the determination of influence the novel synthesized thiosemicarbazide derivative "2-(2-hydroxy-3-methoxybenzylidene) hydrazinecarbothioamide" (HMHC) influenced the corrosion inhibition of mild steel (MS) in a 1.0 M hydrochloric acid acidic solution.This is in an effort to preserve the metal material by maintaining it from corrosion.The synthesized inhibitor was characterized using elemental analysis, and NMR-spectroscopy. Then the corrosion inhibition capability of (HMHC) was studied on mild steel in an acidic medium by weight loss technique within variables [temperature, inhibitor concentration, and time]. The immersion periods were [1:00, 3:00, 5:00, 10:00, 24:00, and 72:00] hours and the tem
... Show MoreIn this research the results of applying Artificial Neural Networks with modified activation function to perform the online and offline identification of four Degrees of Freedom (4-DOF) Selective Compliance Assembly Robot Arm (SCARA) manipulator robot will be described. The proposed model of identification strategy consists of a feed-forward neural network with a modified activation function that operates in parallel with the SCARA robot model. Feed-Forward Neural Networks (FFNN) which have been trained online and offline have been used, without requiring any previous knowledge about the system to be identified. The activation function that is used in the hidden layer in FFNN is a modified version of the wavelet function. This approach ha
... Show MoreIn this research the results of applying Artificial Neural Networks with modified activation function to
perform the online and offline identification of four Degrees of Freedom (4-DOF) Selective Compliance
Assembly Robot Arm (SCARA) manipulator robot will be described. The proposed model of
identification strategy consists of a feed-forward neural network with a modified activation function that
operates in parallel with the SCARA robot model. Feed-Forward Neural Networks (FFNN) which have
been trained online and offline have been used, without requiring any previous knowledge about the
system to be identified. The activation function that is used in the hidden layer in FFNN is a modified
version of the wavelet func
The Sliding Mode Control (SMC) has been among powerful control techniques increasingly. Much attention is paid to both theoretical and practical aspects of disciplines due to their distinctive characteristics such as insensitivity to bounded matched uncertainties, reduction of the order of sliding equations of motion, decoupling mechanical systems design. In the current study, two-link robot performance in the Classical SMC is enhanced via Adaptive Sliding Mode Controller (ASMC) despite uncertainty, external disturbance, and coulomb friction. The key idea is abstracted as follows: switching gains are depressed to the low allowable values, resulting in decreased chattering motion and control's efforts of the two-link robo
... Show MoreThe current research dealt with the study of space compatibility and its role in enhancing the functional aspect of the design of the interior spaces of isolation hospitals by finding a system or format that is compatible with the nature of the changes occurring in the structure and function of the space system, as well as contributing to enhancing compatibility between the functional aspect and the interior space. Therefore, the designer must The interior is the study of the functional and spatial aspects as they are the basic aspects for achieving suitability, and through the interaction between the person and the place, the utilitarian performance characteristics are generated that the interior designer is interested in and tries to d
... Show MoreThe research discussed the propositions of functional structures and the requirements for their transformation according to the variables of use and human interaction through the variables of functions with one form products، multifunctional variables، and transforming form in one product. The patterns of user’s interaction with products were discussed through the variables of functional type، starting from defining the types of functions in the industrial product structures to: practical functions، which were classified into: informational functions، ergonomic functions، use، handling، comfort، global، anthropometric adaptation and physical postures. While the interaction variables were discussed according to the meaning fun
... Show MoreThe subject of demand on oil derivative has occupied an important position at present time in the daily life context. The fuel of benzene and gas oil and kerosene is one of basic elements of that concern, and on local , regional and international levels. The oil derivatives have played a leading role in determining the course and nature of development since early 1970 to the present time whether in the productive Arab countries or the importing. The researcher set out from the hypothesis that the increase of the local consumer demand on some of the oil derivatives is because of the internal and external factors accompanied by the inability of the productive capability and local production to confront this increase, and the resort
... Show MoreHepatitis B virus (HBV) infection is a significant global health problem. Populations of different ethnicities show great heterogeneity in HBV genotype frequency distributions. A cross-sectional study was conducted during June–October 2018 to determine frequency of HBV genotypes among chronic HBV patients from Baghdad, Iraq. The method of detection was nested polymerase chain reaction system. Further, the study assessed the impact of HBV genotypes on serum level of liver-function tests: total serum bilirubin, alkaline phosphatase, alanine aminotransferase and aspartate aminotransferase. Eighty chronic HBV patients were enrolled in the study. Six HBV genotypes were identified (A, B, C, D, E and F). The most frequently encountered genotypes
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