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, some estimators of the unknown shape parameter and reliability function of Basic Gompertz distribution (BGD) have been obtained, such as MLE, UMVUE, and MINMSE, in addition to estimating Bayesian estimators under Scale invariant squared error loss function assuming informative prior represented by Gamma distribution and non-informative prior by using Jefferys prior. Using Monte Carlo simulation method, these estimators of the shape parameter and R(t), have been compared based on mean squared errors and integrated mean squared, respectively
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The physical behavior for the energy distribution function (EDF) of the reactant particles depending upon the gases (fuel) temperature are completely described by a physical model covering the global formulas controlling the EDF profile. Results about the energy distribution for the reactant system indicate a standard EDF, in which it’s arrive a steady state form shape and intern lead to fix the optimum selected temperature.
The aim of this research is to determine the most important and main factors that lead to Preeclampsia. It is also about finding suitable solutions to eradicate these factors and avoid them in order to prevent getting Preeclampsia. To achieve this, a case study sample of (40) patients from Medical City - Oncology Teaching Hospital was used to collect data by a questionnaire which contained (17) reasons to be investigated. The statistical package (SPSS) was used to compare the results of the data analysis through two methods (Radial Bases Function Network) and (Factorial Analysis). Important results were obtained, the two methods determined the same factors that could represent the direct reason which causes Preecla
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The aim of this paper is to present a weak form of -light functions by using -open set which is -light function, and to offer new concepts of disconnected spaces and totally disconnected spaces. The relation between them have been studied. Also, a new form of -totally disconnected and inversely -totally disconnected function have been defined, some examples and facts was submitted.
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The aim of this paper is to approximate multidimensional functions f∈C(R^s) by developing a new type of Feedforward neural networks (FFNS) which we called it Greedy ridge function neural networks (GRGFNNS). Also, we introduce a modification to the greedy algorithm which is used to train the greedy ridge function neural networks. An error bound are introduced in Sobolov space. Finally, a comparison was made between the three algorithms (modified greedy algorithm, Backpropagation algorithm and the result in [1]).
Renal function tests are commonly used in clinical practice to look for renal disease, the most common includes the serum urea, uric acid and creatinine. Heart failure patients have a higher incidence of renal function test abnormalities than individuals who do not have heart failure disease. Fifty subjects of adults (male) were divided in to two groups, 25 subjects (healthy) as control (group1) and 25 subjects with heart failure (group 2). Our results indicate that serum uric acid, urea, and creatinine values were significantly elevated (P≤0.05) in patients group (2) compared with healthy group (1). The results also showed, the effect of age categories on uric acid blood urea nitrogen and creatinine values (P≤0.05) and there were no si
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The aim of this paper is to present a new methodology to find the private key of RSA. A new initial value which is generated from a new equation is selected to speed up the process. In fact, after this value is found, brute force attack is chosen to discover the private key. In addition, for a proposed equation, the multiplier of Euler totient function to find both of the public key and the private key is assigned as 1. Then, it implies that an equation that estimates a new initial value is suitable for the small multiplier. The experimental results show that if all prime factors of the modulus are assigned larger than 3 and the multiplier is 1, the distance between an initial value and the private key
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Nowadays, the field of radionuclide treatment is enjoying an exciting stage and preparing for further growth and progress in the future. For instance, in Asia, the large spread of liver and thyroid diseases has resulted in several new developments/clinical trials using molecular radiotherapy (i.e. targeted radionuclide therapy). Iodine-124 has unique physical properties including long half-life that adding an advantage for pharmacokinetics and radiopharmaceutical analysis. One of its applications in nuclear medicine is in Positron Emission Tomography (PET).
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In this research a new system identification algorithm is presented for obtaining an optimal set of mathematical models for system with perturbed coefficients, then this algorithm is applied practically by an “On Line System Identification Circuit”, based on real time speed response data of a permanent magnet DC motor. Such set of mathematical models represents the physical plant against all variation which may exist in its parameters, and forms a strong mathematical foundation for stability and performance analysis in control theory problems.
his analysis aims to establish Riemann-Liouville derivation andintegral operators regarding the recently suggested seven-parameter Mittag-Leffler function then investigates the corresponding special cases. In addition,certain notable results associated with those new operators have been dis-cussed